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$\arccos (x)$

Langkah 1

Turunan dari $\arccos (x)$ terhadap $x$ adalah $- \frac{1}{\sqrt{1 - x^{2}}}$ .

$f' (x) = - \frac{1}{\sqrt{1 - x^{2}}}$

Langkah 2

Tentukan turunan keduanya.

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Langkah 2.1

Gunakan $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ untuk menuliskan kembali $\sqrt{1 - x^{2}}$ sebagai ${(1 - x^{2})}^{\frac{1}{2}}$ .

$\frac{d}{d x} [- \frac{1}{{(1 - x^{2})}^{\frac{1}{2}}}]$

Langkah 2.2

Diferensialkan menggunakan Kaidah Hasil Kali yang menyatakan bahwa $\frac{d}{d x} [f (x) g (x)]$ adalah $f (x) \frac{d}{d x} [g (x)] + g (x) \frac{d}{d x} [f (x)]$ di mana $f (x) = - 1$ dan $g (x) = \frac{1}{{(1 - x^{2})}^{\frac{1}{2}}}$ .

$- \frac{d}{d x} [\frac{1}{{(1 - x^{2})}^{\frac{1}{2}}}] + \frac{1}{{(1 - x^{2})}^{\frac{1}{2}}} \frac{d}{d x} [- 1]$

Langkah 2.3

Terapkan aturan-aturan dasar eksponen.

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Langkah 2.3.1

Tulis kembali $\frac{1}{{(1 - x^{2})}^{\frac{1}{2}}}$ sebagai ${({(1 - x^{2})}^{\frac{1}{2}})}^{- 1}$ .

$- \frac{d}{d x} [{({(1 - x^{2})}^{\frac{1}{2}})}^{- 1}] + \frac{1}{{(1 - x^{2})}^{\frac{1}{2}}} \frac{d}{d x} [- 1]$

Langkah 2.3.2

Kalikan eksponen dalam ${({(1 - x^{2})}^{\frac{1}{2}})}^{- 1}$ .

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Langkah 2.3.2.1

Terapkan kaidah pangkat dan perkalian eksponen, ${(a^{m})}^{n} = a^{m n}$ .

$- \frac{d}{d x} [{(1 - x^{2})}^{\frac{1}{2} \cdot - 1}] + \frac{1}{{(1 - x^{2})}^{\frac{1}{2}}} \frac{d}{d x} [- 1]$

Langkah 2.3.2.2

Gabungkan $\frac{1}{2}$ dan $- 1$ .

$- \frac{d}{d x} [{(1 - x^{2})}^{\frac{- 1}{2}}] + \frac{1}{{(1 - x^{2})}^{\frac{1}{2}}} \frac{d}{d x} [- 1]$

Langkah 2.3.2.3

Pindahkan tanda negatif di depan pecahan.

$- \frac{d}{d x} [{(1 - x^{2})}^{- \frac{1}{2}}] + \frac{1}{{(1 - x^{2})}^{\frac{1}{2}}} \frac{d}{d x} [- 1]$

Langkah 2.4

Diferensialkan menggunakan kaidah rantai, yang menyatakan bahwa $\frac{d}{d x} [f (g (x))]$ adalah $f' (g (x)) g' (x)$ di mana $f (x) = x^{- \frac{1}{2}}$ dan $g (x) = 1 - x^{2}$ .

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Langkah 2.4.1

Untuk menerapkan Kaidah Rantai, atur $u$ sebagai $1 - x^{2}$ .

$- (\frac{d}{d u} [u^{- \frac{1}{2}}] \frac{d}{d x} [1 - x^{2}]) + \frac{1}{{(1 - x^{2})}^{\frac{1}{2}}} \frac{d}{d x} [- 1]$

Langkah 2.4.2

Diferensialkan menggunakan Kaidah Pangkat yang menyatakan bahwa $\frac{d}{d u} [u^{n}]$ adalah $n u^{n - 1}$ di mana $n = - \frac{1}{2}$ .

$- (- \frac{1}{2} u^{- \frac{1}{2} - 1} \frac{d}{d x} [1 - x^{2}]) + \frac{1}{{(1 - x^{2})}^{\frac{1}{2}}} \frac{d}{d x} [- 1]$

Langkah 2.4.3

Ganti semua kemunculan $u$ dengan $1 - x^{2}$ .

$- (- \frac{1}{2} {(1 - x^{2})}^{- \frac{1}{2} - 1} \frac{d}{d x} [1 - x^{2}]) + \frac{1}{{(1 - x^{2})}^{\frac{1}{2}}} \frac{d}{d x} [- 1]$

Langkah 2.5

Untuk menuliskan $- 1$ sebagai pecahan dengan penyebut umum, kalikan dengan $\frac{2}{2}$ .

$- (- \frac{1}{2} {(1 - x^{2})}^{- \frac{1}{2} - 1 \cdot \frac{2}{2}} \frac{d}{d x} [1 - x^{2}]) + \frac{1}{{(1 - x^{2})}^{\frac{1}{2}}} \frac{d}{d x} [- 1]$

Langkah 2.6

Gabungkan $- 1$ dan $\frac{2}{2}$ .

$- (- \frac{1}{2} {(1 - x^{2})}^{- \frac{1}{2} + \frac{- 1 \cdot 2}{2}} \frac{d}{d x} [1 - x^{2}]) + \frac{1}{{(1 - x^{2})}^{\frac{1}{2}}} \frac{d}{d x} [- 1]$

Langkah 2.7

Gabungkan pembilang dari penyebut persekutuan.

$- (- \frac{1}{2} {(1 - x^{2})}^{\frac{- 1 - 1 \cdot 2}{2}} \frac{d}{d x} [1 - x^{2}]) + \frac{1}{{(1 - x^{2})}^{\frac{1}{2}}} \frac{d}{d x} [- 1]$

Langkah 2.8

Sederhanakan pembilangnya.

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Langkah 2.8.1

Kalikan $- 1$ dengan $2$ .

$- (- \frac{1}{2} {(1 - x^{2})}^{\frac{- 1 - 2}{2}} \frac{d}{d x} [1 - x^{2}]) + \frac{1}{{(1 - x^{2})}^{\frac{1}{2}}} \frac{d}{d x} [- 1]$

Langkah 2.8.2

Kurangi $2$ dengan $- 1$ .

$- (- \frac{1}{2} {(1 - x^{2})}^{\frac{- 3}{2}} \frac{d}{d x} [1 - x^{2}]) + \frac{1}{{(1 - x^{2})}^{\frac{1}{2}}} \frac{d}{d x} [- 1]$

Langkah 2.9

Gabungkan pecahan.

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Langkah 2.9.1

Pindahkan tanda negatif di depan pecahan.

$- (- \frac{1}{2} {(1 - x^{2})}^{- \frac{3}{2}} \frac{d}{d x} [1 - x^{2}]) + \frac{1}{{(1 - x^{2})}^{\frac{1}{2}}} \frac{d}{d x} [- 1]$

Langkah 2.9.2

Gabungkan ${(1 - x^{2})}^{- \frac{3}{2}}$ dan $\frac{1}{2}$ .

$- (- \frac{{(1 - x^{2})}^{- \frac{3}{2}}}{2} \frac{d}{d x} [1 - x^{2}]) + \frac{1}{{(1 - x^{2})}^{\frac{1}{2}}} \frac{d}{d x} [- 1]$

Langkah 2.9.3

Sederhanakan pernyataannya.

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Langkah 2.9.3.1

Pindahkan ${(1 - x^{2})}^{- \frac{3}{2}}$ menjadi penyebut menggunakan aturan eksponen negatif $b^{- n} = \frac{1}{b^{n}}$ .

$- (- \frac{1}{2 {(1 - x^{2})}^{\frac{3}{2}}} \frac{d}{d x} [1 - x^{2}]) + \frac{1}{{(1 - x^{2})}^{\frac{1}{2}}} \frac{d}{d x} [- 1]$

Langkah 2.9.3.2

Kalikan $- 1$ dengan $- 1$ .

$1 (\frac{1}{2 {(1 - x^{2})}^{\frac{3}{2}}} \frac{d}{d x} [1 - x^{2}]) + \frac{1}{{(1 - x^{2})}^{\frac{1}{2}}} \frac{d}{d x} [- 1]$

Langkah 2.9.3.3

Kalikan $\frac{1}{2 {(1 - x^{2})}^{\frac{3}{2}}}$ dengan $1$ .

$\frac{1}{2 {(1 - x^{2})}^{\frac{3}{2}}} \frac{d}{d x} [1 - x^{2}] + \frac{1}{{(1 - x^{2})}^{\frac{1}{2}}} \frac{d}{d x} [- 1]$

Langkah 2.10

Menurut Kaidah Penjumlahan, turunan dari $1 - x^{2}$ terhadap $x$ adalah $\frac{d}{d x} [1] + \frac{d}{d x} [- x^{2}]$ .

$\frac{1}{2 {(1 - x^{2})}^{\frac{3}{2}}} (\frac{d}{d x} [1] + \frac{d}{d x} [- x^{2}]) + \frac{1}{{(1 - x^{2})}^{\frac{1}{2}}} \frac{d}{d x} [- 1]$

Langkah 2.11

Karena $1$ konstan terhadap $x$ , turunan dari $1$ terhadap $x$ adalah $0$ .

$\frac{1}{2 {(1 - x^{2})}^{\frac{3}{2}}} (0 + \frac{d}{d x} [- x^{2}]) + \frac{1}{{(1 - x^{2})}^{\frac{1}{2}}} \frac{d}{d x} [- 1]$

Langkah 2.12

Tambahkan $0$ dan $\frac{d}{d x} [- x^{2}]$ .

$\frac{1}{2 {(1 - x^{2})}^{\frac{3}{2}}} \frac{d}{d x} [- x^{2}] + \frac{1}{{(1 - x^{2})}^{\frac{1}{2}}} \frac{d}{d x} [- 1]$

Langkah 2.13

Karena $- 1$ konstan terhadap $x$ , turunan dari $- x^{2}$ terhadap $x$ adalah $- \frac{d}{d x} [x^{2}]$ .

$\frac{1}{2 {(1 - x^{2})}^{\frac{3}{2}}} (- \frac{d}{d x} [x^{2}]) + \frac{1}{{(1 - x^{2})}^{\frac{1}{2}}} \frac{d}{d x} [- 1]$

Langkah 2.14

Diferensialkan menggunakan Kaidah Pangkat yang menyatakan bahwa $\frac{d}{d x} [x^{n}]$ adalah $n x^{n - 1}$ di mana $n = 2$ .

$\frac{1}{2 {(1 - x^{2})}^{\frac{3}{2}}} (- (2 x)) + \frac{1}{{(1 - x^{2})}^{\frac{1}{2}}} \frac{d}{d x} [- 1]$

Langkah 2.15

Sederhanakan suku-suku.

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Langkah 2.15.1

Kalikan $2$ dengan $- 1$ .

$\frac{1}{2 {(1 - x^{2})}^{\frac{3}{2}}} (- 2 x) + \frac{1}{{(1 - x^{2})}^{\frac{1}{2}}} \frac{d}{d x} [- 1]$

Langkah 2.15.2

Gabungkan $- 2$ dan $\frac{1}{2 {(1 - x^{2})}^{\frac{3}{2}}}$ .

$\frac{- 2}{2 {(1 - x^{2})}^{\frac{3}{2}}} x + \frac{1}{{(1 - x^{2})}^{\frac{1}{2}}} \frac{d}{d x} [- 1]$

Langkah 2.15.3

Gabungkan $\frac{- 2}{2 {(1 - x^{2})}^{\frac{3}{2}}}$ dan $x$ .

$\frac{- 2 x}{2 {(1 - x^{2})}^{\frac{3}{2}}} + \frac{1}{{(1 - x^{2})}^{\frac{1}{2}}} \frac{d}{d x} [- 1]$

Langkah 2.15.4

Faktorkan $2$ dari $- 2 x$ .

$\frac{2 (- x)}{2 {(1 - x^{2})}^{\frac{3}{2}}} + \frac{1}{{(1 - x^{2})}^{\frac{1}{2}}} \frac{d}{d x} [- 1]$

Langkah 2.16

Batalkan faktor persekutuan.

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Langkah 2.16.1

Faktorkan $2$ dari $2 {(1 - x^{2})}^{\frac{3}{2}}$ .

$\frac{2 (- x)}{2 ({(1 - x^{2})}^{\frac{3}{2}})} + \frac{1}{{(1 - x^{2})}^{\frac{1}{2}}} \frac{d}{d x} [- 1]$

Langkah 2.16.2

Batalkan faktor persekutuan.

$\frac{2 (- x)}{2 {(1 - x^{2})}^{\frac{3}{2}}} + \frac{1}{{(1 - x^{2})}^{\frac{1}{2}}} \frac{d}{d x} [- 1]$

Langkah 2.16.3

Tulis kembali pernyataannya.

$\frac{- x}{{(1 - x^{2})}^{\frac{3}{2}}} + \frac{1}{{(1 - x^{2})}^{\frac{1}{2}}} \frac{d}{d x} [- 1]$

Langkah 2.17

Pindahkan tanda negatif di depan pecahan.

$- \frac{x}{{(1 - x^{2})}^{\frac{3}{2}}} + \frac{1}{{(1 - x^{2})}^{\frac{1}{2}}} \frac{d}{d x} [- 1]$

Langkah 2.18

Karena $- 1$ konstan terhadap $x$ , turunan dari $- 1$ terhadap $x$ adalah $0$ .

$- \frac{x}{{(1 - x^{2})}^{\frac{3}{2}}} + \frac{1}{{(1 - x^{2})}^{\frac{1}{2}}} \cdot 0$

Langkah 2.19

Sederhanakan pernyataannya.

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Langkah 2.19.1

Kalikan $\frac{1}{{(1 - x^{2})}^{\frac{1}{2}}}$ dengan $0$ .

$- \frac{x}{{(1 - x^{2})}^{\frac{3}{2}}} + 0$

Langkah 2.19.2

Tambahkan $- \frac{x}{{(1 - x^{2})}^{\frac{3}{2}}}$ dan $0$ .

$f'' (x) = - \frac{x}{{(1 - x^{2})}^{\frac{3}{2}}}$

Langkah 3

Tentukan turunan ketiganya.

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Langkah 3.1

$- \frac{d}{d x} [\frac{x}{{(1 - x^{2})}^{\frac{3}{2}}}] + \frac{x}{{(1 - x^{2})}^{\frac{3}{2}}} \frac{d}{d x} [- 1]$

Langkah 3.2

Diferensialkan menggunakan Kaidah Hasil Bagi yang menyatakan bahwa $\frac{d}{d x} [\frac{f (x)}{g (x)}]$ adalah $\frac{g (x) \frac{d}{d x} [f (x)] - f (x) \frac{d}{d x} [g (x)]}{{g (x)}^{2}}$ di mana $f (x) = x$ dan $g (x) = {(1 - x^{2})}^{\frac{3}{2}}$ .

$- \frac{{(1 - x^{2})}^{\frac{3}{2}} \frac{d}{d x} [x] - x \frac{d}{d x} [{(1 - x^{2})}^{\frac{3}{2}}]}{{({(1 - x^{2})}^{\frac{3}{2}})}^{2}} + \frac{x}{{(1 - x^{2})}^{\frac{3}{2}}} \frac{d}{d x} [- 1]$

Langkah 3.3

Diferensialkan menggunakan Kaidah Pangkat.

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Langkah 3.3.1

Kalikan eksponen dalam ${({(1 - x^{2})}^{\frac{3}{2}})}^{2}$ .

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Langkah 3.3.1.1

Terapkan kaidah pangkat dan perkalian eksponen, ${(a^{m})}^{n} = a^{m n}$ .

$- \frac{{(1 - x^{2})}^{\frac{3}{2}} \frac{d}{d x} [x] - x \frac{d}{d x} [{(1 - x^{2})}^{\frac{3}{2}}]}{{(1 - x^{2})}^{\frac{3}{2} \cdot 2}} + \frac{x}{{(1 - x^{2})}^{\frac{3}{2}}} \frac{d}{d x} [- 1]$

Langkah 3.3.1.2

Batalkan faktor persekutuan dari $2$ .

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Langkah 3.3.1.2.1

Batalkan faktor persekutuan.

Langkah 3.3.1.2.2

Tulis kembali pernyataannya.

$- \frac{{(1 - x^{2})}^{\frac{3}{2}} \frac{d}{d x} [x] - x \frac{d}{d x} [{(1 - x^{2})}^{\frac{3}{2}}]}{{(1 - x^{2})}^{3}} + \frac{x}{{(1 - x^{2})}^{\frac{3}{2}}} \frac{d}{d x} [- 1]$

Langkah 3.3.2

Diferensialkan menggunakan Kaidah Pangkat yang menyatakan bahwa $\frac{d}{d x} [x^{n}]$ adalah $n x^{n - 1}$ di mana $n = 1$ .

$- \frac{{(1 - x^{2})}^{\frac{3}{2}} \cdot 1 - x \frac{d}{d x} [{(1 - x^{2})}^{\frac{3}{2}}]}{{(1 - x^{2})}^{3}} + \frac{x}{{(1 - x^{2})}^{\frac{3}{2}}} \frac{d}{d x} [- 1]$

Langkah 3.3.3

Kalikan ${(1 - x^{2})}^{\frac{3}{2}}$ dengan $1$ .

$- \frac{{(1 - x^{2})}^{\frac{3}{2}} - x \frac{d}{d x} [{(1 - x^{2})}^{\frac{3}{2}}]}{{(1 - x^{2})}^{3}} + \frac{x}{{(1 - x^{2})}^{\frac{3}{2}}} \frac{d}{d x} [- 1]$

Langkah 3.4

Diferensialkan menggunakan kaidah rantai, yang menyatakan bahwa $\frac{d}{d x} [f (g (x))]$ adalah $f' (g (x)) g' (x)$ di mana $f (x) = x^{\frac{3}{2}}$ dan $g (x) = 1 - x^{2}$ .

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Langkah 3.4.1

Untuk menerapkan Kaidah Rantai, atur $u$ sebagai $1 - x^{2}$ .

$- \frac{{(1 - x^{2})}^{\frac{3}{2}} - x (\frac{d}{d u} [u^{\frac{3}{2}}] \frac{d}{d x} [1 - x^{2}])}{{(1 - x^{2})}^{3}} + \frac{x}{{(1 - x^{2})}^{\frac{3}{2}}} \frac{d}{d x} [- 1]$

Langkah 3.4.2

Diferensialkan menggunakan Kaidah Pangkat yang menyatakan bahwa $\frac{d}{d u} [u^{n}]$ adalah $n u^{n - 1}$ di mana $n = \frac{3}{2}$ .

$- \frac{{(1 - x^{2})}^{\frac{3}{2}} - x (\frac{3}{2} u^{\frac{3}{2} - 1} \frac{d}{d x} [1 - x^{2}])}{{(1 - x^{2})}^{3}} + \frac{x}{{(1 - x^{2})}^{\frac{3}{2}}} \frac{d}{d x} [- 1]$

Langkah 3.4.3

Ganti semua kemunculan $u$ dengan $1 - x^{2}$ .

$- \frac{{(1 - x^{2})}^{\frac{3}{2}} - x (\frac{3}{2} {(1 - x^{2})}^{\frac{3}{2} - 1} \frac{d}{d x} [1 - x^{2}])}{{(1 - x^{2})}^{3}} + \frac{x}{{(1 - x^{2})}^{\frac{3}{2}}} \frac{d}{d x} [- 1]$

Langkah 3.5

Untuk menuliskan $- 1$ sebagai pecahan dengan penyebut umum, kalikan dengan $\frac{2}{2}$ .

$- \frac{{(1 - x^{2})}^{\frac{3}{2}} - x (\frac{3}{2} {(1 - x^{2})}^{\frac{3}{2} - 1 \cdot \frac{2}{2}} \frac{d}{d x} [1 - x^{2}])}{{(1 - x^{2})}^{3}} + \frac{x}{{(1 - x^{2})}^{\frac{3}{2}}} \frac{d}{d x} [- 1]$

Langkah 3.6

Gabungkan $- 1$ dan $\frac{2}{2}$ .

$- \frac{{(1 - x^{2})}^{\frac{3}{2}} - x (\frac{3}{2} {(1 - x^{2})}^{\frac{3}{2} + \frac{- 1 \cdot 2}{2}} \frac{d}{d x} [1 - x^{2}])}{{(1 - x^{2})}^{3}} + \frac{x}{{(1 - x^{2})}^{\frac{3}{2}}} \frac{d}{d x} [- 1]$

Langkah 3.7

Gabungkan pembilang dari penyebut persekutuan.

$- \frac{{(1 - x^{2})}^{\frac{3}{2}} - x (\frac{3}{2} {(1 - x^{2})}^{\frac{3 - 1 \cdot 2}{2}} \frac{d}{d x} [1 - x^{2}])}{{(1 - x^{2})}^{3}} + \frac{x}{{(1 - x^{2})}^{\frac{3}{2}}} \frac{d}{d x} [- 1]$

Langkah 3.8

Sederhanakan pembilangnya.

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Langkah 3.8.1

Kalikan $- 1$ dengan $2$ .

$- \frac{{(1 - x^{2})}^{\frac{3}{2}} - x (\frac{3}{2} {(1 - x^{2})}^{\frac{3 - 2}{2}} \frac{d}{d x} [1 - x^{2}])}{{(1 - x^{2})}^{3}} + \frac{x}{{(1 - x^{2})}^{\frac{3}{2}}} \frac{d}{d x} [- 1]$

Langkah 3.8.2

Kurangi $2$ dengan $3$ .

$- \frac{{(1 - x^{2})}^{\frac{3}{2}} - x (\frac{3}{2} {(1 - x^{2})}^{\frac{1}{2}} \frac{d}{d x} [1 - x^{2}])}{{(1 - x^{2})}^{3}} + \frac{x}{{(1 - x^{2})}^{\frac{3}{2}}} \frac{d}{d x} [- 1]$

Langkah 3.9

Gabungkan pecahan.

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Langkah 3.9.1

Gabungkan $\frac{3}{2}$ dan ${(1 - x^{2})}^{\frac{1}{2}}$ .

$- \frac{{(1 - x^{2})}^{\frac{3}{2}} - x (\frac{3 {(1 - x^{2})}^{\frac{1}{2}}}{2} \frac{d}{d x} [1 - x^{2}])}{{(1 - x^{2})}^{3}} + \frac{x}{{(1 - x^{2})}^{\frac{3}{2}}} \frac{d}{d x} [- 1]$

Langkah 3.9.2

Gabungkan $\frac{3 {(1 - x^{2})}^{\frac{1}{2}}}{2}$ dan $x$ .

$- \frac{{(1 - x^{2})}^{\frac{3}{2}} - \frac{3 {(1 - x^{2})}^{\frac{1}{2}} x}{2} \frac{d}{d x} [1 - x^{2}]}{{(1 - x^{2})}^{3}} + \frac{x}{{(1 - x^{2})}^{\frac{3}{2}}} \frac{d}{d x} [- 1]$

Langkah 3.10

Menurut Kaidah Penjumlahan, turunan dari $1 - x^{2}$ terhadap $x$ adalah $\frac{d}{d x} [1] + \frac{d}{d x} [- x^{2}]$ .

$- \frac{{(1 - x^{2})}^{\frac{3}{2}} - \frac{3 {(1 - x^{2})}^{\frac{1}{2}} x}{2} (\frac{d}{d x} [1] + \frac{d}{d x} [- x^{2}])}{{(1 - x^{2})}^{3}} + \frac{x}{{(1 - x^{2})}^{\frac{3}{2}}} \frac{d}{d x} [- 1]$

Langkah 3.11

Karena $1$ konstan terhadap $x$ , turunan dari $1$ terhadap $x$ adalah $0$ .

$- \frac{{(1 - x^{2})}^{\frac{3}{2}} - \frac{3 {(1 - x^{2})}^{\frac{1}{2}} x}{2} (0 + \frac{d}{d x} [- x^{2}])}{{(1 - x^{2})}^{3}} + \frac{x}{{(1 - x^{2})}^{\frac{3}{2}}} \frac{d}{d x} [- 1]$

Langkah 3.12

Tambahkan $0$ dan $\frac{d}{d x} [- x^{2}]$ .

$- \frac{{(1 - x^{2})}^{\frac{3}{2}} - \frac{3 {(1 - x^{2})}^{\frac{1}{2}} x}{2} \frac{d}{d x} [- x^{2}]}{{(1 - x^{2})}^{3}} + \frac{x}{{(1 - x^{2})}^{\frac{3}{2}}} \frac{d}{d x} [- 1]$

Langkah 3.13

Karena $- 1$ konstan terhadap $x$ , turunan dari $- x^{2}$ terhadap $x$ adalah $- \frac{d}{d x} [x^{2}]$ .

$- \frac{{(1 - x^{2})}^{\frac{3}{2}} - \frac{3 {(1 - x^{2})}^{\frac{1}{2}} x}{2} (- \frac{d}{d x} [x^{2}])}{{(1 - x^{2})}^{3}} + \frac{x}{{(1 - x^{2})}^{\frac{3}{2}}} \frac{d}{d x} [- 1]$

Langkah 3.14

Kalikan.

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Langkah 3.14.1

Kalikan $- 1$ dengan $- 1$ .

$- \frac{{(1 - x^{2})}^{\frac{3}{2}} + 1 \frac{3 {(1 - x^{2})}^{\frac{1}{2}} x}{2} \frac{d}{d x} [x^{2}]}{{(1 - x^{2})}^{3}} + \frac{x}{{(1 - x^{2})}^{\frac{3}{2}}} \frac{d}{d x} [- 1]$

Langkah 3.14.2

Kalikan $\frac{3 {(1 - x^{2})}^{\frac{1}{2}} x}{2}$ dengan $1$ .

$- \frac{{(1 - x^{2})}^{\frac{3}{2}} + \frac{3 {(1 - x^{2})}^{\frac{1}{2}} x}{2} \frac{d}{d x} [x^{2}]}{{(1 - x^{2})}^{3}} + \frac{x}{{(1 - x^{2})}^{\frac{3}{2}}} \frac{d}{d x} [- 1]$

Langkah 3.15

Diferensialkan menggunakan Kaidah Pangkat yang menyatakan bahwa $\frac{d}{d x} [x^{n}]$ adalah $n x^{n - 1}$ di mana $n = 2$ .

$- \frac{{(1 - x^{2})}^{\frac{3}{2}} + \frac{3 {(1 - x^{2})}^{\frac{1}{2}} x}{2} (2 x)}{{(1 - x^{2})}^{3}} + \frac{x}{{(1 - x^{2})}^{\frac{3}{2}}} \frac{d}{d x} [- 1]$

Langkah 3.16

Gabungkan pecahan.

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Langkah 3.16.1

Gabungkan $2$ dan $\frac{3 {(1 - x^{2})}^{\frac{1}{2}} x}{2}$ .

$- \frac{{(1 - x^{2})}^{\frac{3}{2}} + \frac{2 (3 {(1 - x^{2})}^{\frac{1}{2}} x)}{2} x}{{(1 - x^{2})}^{3}} + \frac{x}{{(1 - x^{2})}^{\frac{3}{2}}} \frac{d}{d x} [- 1]$

Langkah 3.16.2

Kalikan $3$ dengan $2$ .

$- \frac{{(1 - x^{2})}^{\frac{3}{2}} + \frac{6 ({(1 - x^{2})}^{\frac{1}{2}} x)}{2} x}{{(1 - x^{2})}^{3}} + \frac{x}{{(1 - x^{2})}^{\frac{3}{2}}} \frac{d}{d x} [- 1]$

Langkah 3.16.3

Gabungkan $\frac{6 ({(1 - x^{2})}^{\frac{1}{2}} x)}{2}$ dan $x$ .

$- \frac{{(1 - x^{2})}^{\frac{3}{2}} + \frac{6 ({(1 - x^{2})}^{\frac{1}{2}} x) x}{2}}{{(1 - x^{2})}^{3}} + \frac{x}{{(1 - x^{2})}^{\frac{3}{2}}} \frac{d}{d x} [- 1]$

Langkah 3.17

Naikkan $x$ menjadi pangkat $1$ .

$- \frac{{(1 - x^{2})}^{\frac{3}{2}} + \frac{6 ({(1 - x^{2})}^{\frac{1}{2}} (x^{1} x))}{2}}{{(1 - x^{2})}^{3}} + \frac{x}{{(1 - x^{2})}^{\frac{3}{2}}} \frac{d}{d x} [- 1]$

Langkah 3.18

Naikkan $x$ menjadi pangkat $1$ .

$- \frac{{(1 - x^{2})}^{\frac{3}{2}} + \frac{6 ({(1 - x^{2})}^{\frac{1}{2}} (x^{1} x^{1}))}{2}}{{(1 - x^{2})}^{3}} + \frac{x}{{(1 - x^{2})}^{\frac{3}{2}}} \frac{d}{d x} [- 1]$

Langkah 3.19

Gunakan kaidah pangkat $a^{m} a^{n} = a^{m + n}$ untuk menggabungkan pangkat.

$- \frac{{(1 - x^{2})}^{\frac{3}{2}} + \frac{6 ({(1 - x^{2})}^{\frac{1}{2}} x^{1 + 1})}{2}}{{(1 - x^{2})}^{3}} + \frac{x}{{(1 - x^{2})}^{\frac{3}{2}}} \frac{d}{d x} [- 1]$

Langkah 3.20

Tambahkan $1$ dan $1$ .

$- \frac{{(1 - x^{2})}^{\frac{3}{2}} + \frac{6 ({(1 - x^{2})}^{\frac{1}{2}} x^{2})}{2}}{{(1 - x^{2})}^{3}} + \frac{x}{{(1 - x^{2})}^{\frac{3}{2}}} \frac{d}{d x} [- 1]$

Langkah 3.21

Faktorkan $2$ dari $6 {(1 - x^{2})}^{\frac{1}{2}} x^{2}$ .

$- \frac{{(1 - x^{2})}^{\frac{3}{2}} + \frac{2 (3 {(1 - x^{2})}^{\frac{1}{2}} x^{2})}{2}}{{(1 - x^{2})}^{3}} + \frac{x}{{(1 - x^{2})}^{\frac{3}{2}}} \frac{d}{d x} [- 1]$

Langkah 3.22

Batalkan faktor persekutuan.

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Langkah 3.22.1

Faktorkan $2$ dari $2$ .

$- \frac{{(1 - x^{2})}^{\frac{3}{2}} + \frac{2 (3 {(1 - x^{2})}^{\frac{1}{2}} x^{2})}{2 (1)}}{{(1 - x^{2})}^{3}} + \frac{x}{{(1 - x^{2})}^{\frac{3}{2}}} \frac{d}{d x} [- 1]$

Langkah 3.22.2

Batalkan faktor persekutuan.

$- \frac{{(1 - x^{2})}^{\frac{3}{2}} + \frac{2 (3 {(1 - x^{2})}^{\frac{1}{2}} x^{2})}{2 \cdot 1}}{{(1 - x^{2})}^{3}} + \frac{x}{{(1 - x^{2})}^{\frac{3}{2}}} \frac{d}{d x} [- 1]$

Langkah 3.22.3

Tulis kembali pernyataannya.

$- \frac{{(1 - x^{2})}^{\frac{3}{2}} + \frac{3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{1}}{{(1 - x^{2})}^{3}} + \frac{x}{{(1 - x^{2})}^{\frac{3}{2}}} \frac{d}{d x} [- 1]$

Langkah 3.22.4

Bagilah $3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}$ dengan $1$ .

$- \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} + \frac{x}{{(1 - x^{2})}^{\frac{3}{2}}} \frac{d}{d x} [- 1]$

Langkah 3.23

Karena $- 1$ konstan terhadap $x$ , turunan dari $- 1$ terhadap $x$ adalah $0$ .

$- \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} + \frac{x}{{(1 - x^{2})}^{\frac{3}{2}}} \cdot 0$

Langkah 3.24

Sederhanakan pernyataannya.

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Langkah 3.24.1

Kalikan $\frac{x}{{(1 - x^{2})}^{\frac{3}{2}}}$ dengan $0$ .

$- \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} + 0$

Langkah 3.24.2

Tambahkan $- \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}}$ dan $0$ .

$f''' (x) = - \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}}$

Langkah 4

Cari turunan keempat.

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Langkah 4.1

$- \frac{d}{d x} [\frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}}] + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.2

$- \frac{{(1 - x^{2})}^{3} \frac{d}{d x} [{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}] - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{({(1 - x^{2})}^{3})}^{2}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.3

Diferensialkan menggunakan Kaidah Penjumlahan.

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Langkah 4.3.1

Kalikan eksponen dalam ${({(1 - x^{2})}^{3})}^{2}$ .

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Langkah 4.3.1.1

Terapkan kaidah pangkat dan perkalian eksponen, ${(a^{m})}^{n} = a^{m n}$ .

$- \frac{{(1 - x^{2})}^{3} \frac{d}{d x} [{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}] - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{3 \cdot 2}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.3.1.2

Kalikan $3$ dengan $2$ .

$- \frac{{(1 - x^{2})}^{3} \frac{d}{d x} [{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}] - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.3.2

Menurut Kaidah Penjumlahan, turunan dari ${(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}$ terhadap $x$ adalah $\frac{d}{d x} [{(1 - x^{2})}^{\frac{3}{2}}] + \frac{d}{d x} [3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}]$ .

$- \frac{{(1 - x^{2})}^{3} (\frac{d}{d x} [{(1 - x^{2})}^{\frac{3}{2}}] + \frac{d}{d x} [3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}]) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.4

Diferensialkan menggunakan kaidah rantai, yang menyatakan bahwa $\frac{d}{d x} [f (g (x))]$ adalah $f' (g (x)) g' (x)$ di mana $f (x) = x^{\frac{3}{2}}$ dan $g (x) = 1 - x^{2}$ .

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Langkah 4.4.1

Untuk menerapkan Kaidah Rantai, atur $u_{1}$ sebagai $1 - x^{2}$ .

$- \frac{{(1 - x^{2})}^{3} (\frac{d}{d u_{1}} [{u_{1}}^{\frac{3}{2}}] \frac{d}{d x} [1 - x^{2}] + \frac{d}{d x} [3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}]) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.4.2

Diferensialkan menggunakan Kaidah Pangkat yang menyatakan bahwa $\frac{d}{d u_{1}} [{u_{1}}^{n}]$ adalah $n {u_{1}}^{n - 1}$ di mana $n = \frac{3}{2}$ .

$- \frac{{(1 - x^{2})}^{3} (\frac{3}{2} {u_{1}}^{\frac{3}{2} - 1} \frac{d}{d x} [1 - x^{2}] + \frac{d}{d x} [3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}]) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.4.3

Ganti semua kemunculan $u_{1}$ dengan $1 - x^{2}$ .

$- \frac{{(1 - x^{2})}^{3} (\frac{3}{2} {(1 - x^{2})}^{\frac{3}{2} - 1} \frac{d}{d x} [1 - x^{2}] + \frac{d}{d x} [3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}]) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.5

Untuk menuliskan $- 1$ sebagai pecahan dengan penyebut umum, kalikan dengan $\frac{2}{2}$ .

$- \frac{{(1 - x^{2})}^{3} (\frac{3}{2} {(1 - x^{2})}^{\frac{3}{2} - 1 \cdot \frac{2}{2}} \frac{d}{d x} [1 - x^{2}] + \frac{d}{d x} [3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}]) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.6

Gabungkan $- 1$ dan $\frac{2}{2}$ .

$- \frac{{(1 - x^{2})}^{3} (\frac{3}{2} {(1 - x^{2})}^{\frac{3}{2} + \frac{- 1 \cdot 2}{2}} \frac{d}{d x} [1 - x^{2}] + \frac{d}{d x} [3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}]) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.7

Gabungkan pembilang dari penyebut persekutuan.

$- \frac{{(1 - x^{2})}^{3} (\frac{3}{2} {(1 - x^{2})}^{\frac{3 - 1 \cdot 2}{2}} \frac{d}{d x} [1 - x^{2}] + \frac{d}{d x} [3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}]) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.8

Sederhanakan pembilangnya.

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Langkah 4.8.1

Kalikan $- 1$ dengan $2$ .

$- \frac{{(1 - x^{2})}^{3} (\frac{3}{2} {(1 - x^{2})}^{\frac{3 - 2}{2}} \frac{d}{d x} [1 - x^{2}] + \frac{d}{d x} [3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}]) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.8.2

Kurangi $2$ dengan $3$ .

$- \frac{{(1 - x^{2})}^{3} (\frac{3}{2} {(1 - x^{2})}^{\frac{1}{2}} \frac{d}{d x} [1 - x^{2}] + \frac{d}{d x} [3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}]) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.9

Gabungkan $\frac{3}{2}$ dan ${(1 - x^{2})}^{\frac{1}{2}}$ .

$- \frac{{(1 - x^{2})}^{3} (\frac{3 {(1 - x^{2})}^{\frac{1}{2}}}{2} \frac{d}{d x} [1 - x^{2}] + \frac{d}{d x} [3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}]) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.10

Menurut Kaidah Penjumlahan, turunan dari $1 - x^{2}$ terhadap $x$ adalah $\frac{d}{d x} [1] + \frac{d}{d x} [- x^{2}]$ .

$- \frac{{(1 - x^{2})}^{3} (\frac{3 {(1 - x^{2})}^{\frac{1}{2}}}{2} (\frac{d}{d x} [1] + \frac{d}{d x} [- x^{2}]) + \frac{d}{d x} [3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}]) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.11

Karena $1$ konstan terhadap $x$ , turunan dari $1$ terhadap $x$ adalah $0$ .

$- \frac{{(1 - x^{2})}^{3} (\frac{3 {(1 - x^{2})}^{\frac{1}{2}}}{2} (0 + \frac{d}{d x} [- x^{2}]) + \frac{d}{d x} [3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}]) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.12

Tambahkan $0$ dan $\frac{d}{d x} [- x^{2}]$ .

$- \frac{{(1 - x^{2})}^{3} (\frac{3 {(1 - x^{2})}^{\frac{1}{2}}}{2} \frac{d}{d x} [- x^{2}] + \frac{d}{d x} [3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}]) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.13

Karena $- 1$ konstan terhadap $x$ , turunan dari $- x^{2}$ terhadap $x$ adalah $- \frac{d}{d x} [x^{2}]$ .

$- \frac{{(1 - x^{2})}^{3} (\frac{3 {(1 - x^{2})}^{\frac{1}{2}}}{2} (- \frac{d}{d x} [x^{2}]) + \frac{d}{d x} [3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}]) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.14

Diferensialkan menggunakan Kaidah Pangkat yang menyatakan bahwa $\frac{d}{d x} [x^{n}]$ adalah $n x^{n - 1}$ di mana $n = 2$ .

$- \frac{{(1 - x^{2})}^{3} (\frac{3 {(1 - x^{2})}^{\frac{1}{2}}}{2} (- (2 x)) + \frac{d}{d x} [3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}]) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.15

Sederhanakan suku-suku.

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Langkah 4.15.1

Kalikan $2$ dengan $- 1$ .

$- \frac{{(1 - x^{2})}^{3} (\frac{3 {(1 - x^{2})}^{\frac{1}{2}}}{2} (- 2 x) + \frac{d}{d x} [3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}]) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.15.2

Gabungkan $- 2$ dan $\frac{3 {(1 - x^{2})}^{\frac{1}{2}}}{2}$ .

$- \frac{{(1 - x^{2})}^{3} (\frac{- 2 (3 {(1 - x^{2})}^{\frac{1}{2}})}{2} x + \frac{d}{d x} [3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}]) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.15.3

Kalikan $3$ dengan $- 2$ .

$- \frac{{(1 - x^{2})}^{3} (\frac{- 6 {(1 - x^{2})}^{\frac{1}{2}}}{2} x + \frac{d}{d x} [3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}]) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.15.4

Gabungkan $\frac{- 6 {(1 - x^{2})}^{\frac{1}{2}}}{2}$ dan $x$ .

$- \frac{{(1 - x^{2})}^{3} (\frac{- 6 {(1 - x^{2})}^{\frac{1}{2}} x}{2} + \frac{d}{d x} [3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}]) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.15.5

Faktorkan $2$ dari $- 6 {(1 - x^{2})}^{\frac{1}{2}} x$ .

$- \frac{{(1 - x^{2})}^{3} (\frac{2 (- 3 {(1 - x^{2})}^{\frac{1}{2}} x)}{2} + \frac{d}{d x} [3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}]) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.16

Batalkan faktor persekutuan.

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Langkah 4.16.1

Faktorkan $2$ dari $2$ .

$- \frac{{(1 - x^{2})}^{3} (\frac{2 (- 3 {(1 - x^{2})}^{\frac{1}{2}} x)}{2 (1)} + \frac{d}{d x} [3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}]) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.16.2

Batalkan faktor persekutuan.

$- \frac{{(1 - x^{2})}^{3} (\frac{2 (- 3 {(1 - x^{2})}^{\frac{1}{2}} x)}{2 \cdot 1} + \frac{d}{d x} [3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}]) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.16.3

Tulis kembali pernyataannya.

$- \frac{{(1 - x^{2})}^{3} (\frac{- 3 {(1 - x^{2})}^{\frac{1}{2}} x}{1} + \frac{d}{d x} [3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}]) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.16.4

Bagilah $- 3 {(1 - x^{2})}^{\frac{1}{2}} x$ dengan $1$ .

$- \frac{{(1 - x^{2})}^{3} (- 3 {(1 - x^{2})}^{\frac{1}{2}} x + \frac{d}{d x} [3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}]) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.17

Karena $3$ konstan terhadap $x$ , turunan dari $3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}$ terhadap $x$ adalah $3 \frac{d}{d x} [{(1 - x^{2})}^{\frac{1}{2}} x^{2}]$ .

$- \frac{{(1 - x^{2})}^{3} (- 3 {(1 - x^{2})}^{\frac{1}{2}} x + 3 \frac{d}{d x} [{(1 - x^{2})}^{\frac{1}{2}} x^{2}]) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.18

Diferensialkan menggunakan Kaidah Hasil Kali yang menyatakan bahwa $\frac{d}{d x} [f (x) g (x)]$ adalah $f (x) \frac{d}{d x} [g (x)] + g (x) \frac{d}{d x} [f (x)]$ di mana $f (x) = {(1 - x^{2})}^{\frac{1}{2}}$ dan $g (x) = x^{2}$ .

$- \frac{{(1 - x^{2})}^{3} (- 3 {(1 - x^{2})}^{\frac{1}{2}} x + 3 ({(1 - x^{2})}^{\frac{1}{2}} \frac{d}{d x} [x^{2}] + x^{2} \frac{d}{d x} [{(1 - x^{2})}^{\frac{1}{2}}])) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.19

Diferensialkan menggunakan Kaidah Pangkat.

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Langkah 4.19.1

Diferensialkan menggunakan Kaidah Pangkat yang menyatakan bahwa $\frac{d}{d x} [x^{n}]$ adalah $n x^{n - 1}$ di mana $n = 2$ .

$- \frac{{(1 - x^{2})}^{3} (- 3 {(1 - x^{2})}^{\frac{1}{2}} x + 3 ({(1 - x^{2})}^{\frac{1}{2}} (2 x) + x^{2} \frac{d}{d x} [{(1 - x^{2})}^{\frac{1}{2}}])) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.19.2

Pindahkan $2$ ke sebelah kiri ${(1 - x^{2})}^{\frac{1}{2}}$ .

$- \frac{{(1 - x^{2})}^{3} (- 3 {(1 - x^{2})}^{\frac{1}{2}} x + 3 (2 \cdot {(1 - x^{2})}^{\frac{1}{2}} x + x^{2} \frac{d}{d x} [{(1 - x^{2})}^{\frac{1}{2}}])) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.20

Diferensialkan menggunakan kaidah rantai, yang menyatakan bahwa $\frac{d}{d x} [f (g (x))]$ adalah $f' (g (x)) g' (x)$ di mana $f (x) = x^{\frac{1}{2}}$ dan $g (x) = 1 - x^{2}$ .

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Langkah 4.20.1

Untuk menerapkan Kaidah Rantai, atur $u_{2}$ sebagai $1 - x^{2}$ .

$- \frac{{(1 - x^{2})}^{3} (- 3 {(1 - x^{2})}^{\frac{1}{2}} x + 3 (2 {(1 - x^{2})}^{\frac{1}{2}} x + x^{2} (\frac{d}{d u_{2}} [{u_{2}}^{\frac{1}{2}}] \frac{d}{d x} [1 - x^{2}]))) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.20.2

Diferensialkan menggunakan Kaidah Pangkat yang menyatakan bahwa $\frac{d}{d u_{2}} [{u_{2}}^{n}]$ adalah $n {u_{2}}^{n - 1}$ di mana $n = \frac{1}{2}$ .

$- \frac{{(1 - x^{2})}^{3} (- 3 {(1 - x^{2})}^{\frac{1}{2}} x + 3 (2 {(1 - x^{2})}^{\frac{1}{2}} x + x^{2} (\frac{1}{2} {u_{2}}^{\frac{1}{2} - 1} \frac{d}{d x} [1 - x^{2}]))) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.20.3

Ganti semua kemunculan $u_{2}$ dengan $1 - x^{2}$ .

$- \frac{{(1 - x^{2})}^{3} (- 3 {(1 - x^{2})}^{\frac{1}{2}} x + 3 (2 {(1 - x^{2})}^{\frac{1}{2}} x + x^{2} (\frac{1}{2} {(1 - x^{2})}^{\frac{1}{2} - 1} \frac{d}{d x} [1 - x^{2}]))) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.21

Untuk menuliskan $- 1$ sebagai pecahan dengan penyebut umum, kalikan dengan $\frac{2}{2}$ .

$- \frac{{(1 - x^{2})}^{3} (- 3 {(1 - x^{2})}^{\frac{1}{2}} x + 3 (2 {(1 - x^{2})}^{\frac{1}{2}} x + x^{2} (\frac{1}{2} {(1 - x^{2})}^{\frac{1}{2} - 1 \cdot \frac{2}{2}} \frac{d}{d x} [1 - x^{2}]))) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.22

Gabungkan $- 1$ dan $\frac{2}{2}$ .

$- \frac{{(1 - x^{2})}^{3} (- 3 {(1 - x^{2})}^{\frac{1}{2}} x + 3 (2 {(1 - x^{2})}^{\frac{1}{2}} x + x^{2} (\frac{1}{2} {(1 - x^{2})}^{\frac{1}{2} + \frac{- 1 \cdot 2}{2}} \frac{d}{d x} [1 - x^{2}]))) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.23

Gabungkan pembilang dari penyebut persekutuan.

$- \frac{{(1 - x^{2})}^{3} (- 3 {(1 - x^{2})}^{\frac{1}{2}} x + 3 (2 {(1 - x^{2})}^{\frac{1}{2}} x + x^{2} (\frac{1}{2} {(1 - x^{2})}^{\frac{1 - 1 \cdot 2}{2}} \frac{d}{d x} [1 - x^{2}]))) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.24

Sederhanakan pembilangnya.

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Langkah 4.24.1

Kalikan $- 1$ dengan $2$ .

$- \frac{{(1 - x^{2})}^{3} (- 3 {(1 - x^{2})}^{\frac{1}{2}} x + 3 (2 {(1 - x^{2})}^{\frac{1}{2}} x + x^{2} (\frac{1}{2} {(1 - x^{2})}^{\frac{1 - 2}{2}} \frac{d}{d x} [1 - x^{2}]))) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.24.2

Kurangi $2$ dengan $1$ .

$- \frac{{(1 - x^{2})}^{3} (- 3 {(1 - x^{2})}^{\frac{1}{2}} x + 3 (2 {(1 - x^{2})}^{\frac{1}{2}} x + x^{2} (\frac{1}{2} {(1 - x^{2})}^{\frac{- 1}{2}} \frac{d}{d x} [1 - x^{2}]))) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.25

Gabungkan pecahan.

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Langkah 4.25.1

Pindahkan tanda negatif di depan pecahan.

$- \frac{{(1 - x^{2})}^{3} (- 3 {(1 - x^{2})}^{\frac{1}{2}} x + 3 (2 {(1 - x^{2})}^{\frac{1}{2}} x + x^{2} (\frac{1}{2} {(1 - x^{2})}^{- \frac{1}{2}} \frac{d}{d x} [1 - x^{2}]))) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.25.2

Gabungkan $\frac{1}{2}$ dan ${(1 - x^{2})}^{- \frac{1}{2}}$ .

$- \frac{{(1 - x^{2})}^{3} (- 3 {(1 - x^{2})}^{\frac{1}{2}} x + 3 (2 {(1 - x^{2})}^{\frac{1}{2}} x + x^{2} (\frac{{(1 - x^{2})}^{- \frac{1}{2}}}{2} \frac{d}{d x} [1 - x^{2}]))) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.25.3

Pindahkan ${(1 - x^{2})}^{- \frac{1}{2}}$ menjadi penyebut menggunakan aturan eksponen negatif $b^{- n} = \frac{1}{b^{n}}$ .

$- \frac{{(1 - x^{2})}^{3} (- 3 {(1 - x^{2})}^{\frac{1}{2}} x + 3 (2 {(1 - x^{2})}^{\frac{1}{2}} x + x^{2} (\frac{1}{2 {(1 - x^{2})}^{\frac{1}{2}}} \frac{d}{d x} [1 - x^{2}]))) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.25.4

Gabungkan $\frac{1}{2 {(1 - x^{2})}^{\frac{1}{2}}}$ dan $x^{2}$ .

$- \frac{{(1 - x^{2})}^{3} (- 3 {(1 - x^{2})}^{\frac{1}{2}} x + 3 (2 {(1 - x^{2})}^{\frac{1}{2}} x + \frac{x^{2}}{2 {(1 - x^{2})}^{\frac{1}{2}}} \frac{d}{d x} [1 - x^{2}])) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.26

Menurut Kaidah Penjumlahan, turunan dari $1 - x^{2}$ terhadap $x$ adalah $\frac{d}{d x} [1] + \frac{d}{d x} [- x^{2}]$ .

$- \frac{{(1 - x^{2})}^{3} (- 3 {(1 - x^{2})}^{\frac{1}{2}} x + 3 (2 {(1 - x^{2})}^{\frac{1}{2}} x + \frac{x^{2}}{2 {(1 - x^{2})}^{\frac{1}{2}}} (\frac{d}{d x} [1] + \frac{d}{d x} [- x^{2}]))) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.27

Karena $1$ konstan terhadap $x$ , turunan dari $1$ terhadap $x$ adalah $0$ .

$- \frac{{(1 - x^{2})}^{3} (- 3 {(1 - x^{2})}^{\frac{1}{2}} x + 3 (2 {(1 - x^{2})}^{\frac{1}{2}} x + \frac{x^{2}}{2 {(1 - x^{2})}^{\frac{1}{2}}} (0 + \frac{d}{d x} [- x^{2}]))) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.28

Tambahkan $0$ dan $\frac{d}{d x} [- x^{2}]$ .

$- \frac{{(1 - x^{2})}^{3} (- 3 {(1 - x^{2})}^{\frac{1}{2}} x + 3 (2 {(1 - x^{2})}^{\frac{1}{2}} x + \frac{x^{2}}{2 {(1 - x^{2})}^{\frac{1}{2}}} \frac{d}{d x} [- x^{2}])) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.29

Karena $- 1$ konstan terhadap $x$ , turunan dari $- x^{2}$ terhadap $x$ adalah $- \frac{d}{d x} [x^{2}]$ .

$- \frac{{(1 - x^{2})}^{3} (- 3 {(1 - x^{2})}^{\frac{1}{2}} x + 3 (2 {(1 - x^{2})}^{\frac{1}{2}} x + \frac{x^{2}}{2 {(1 - x^{2})}^{\frac{1}{2}}} (- \frac{d}{d x} [x^{2}]))) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.30

Diferensialkan menggunakan Kaidah Pangkat yang menyatakan bahwa $\frac{d}{d x} [x^{n}]$ adalah $n x^{n - 1}$ di mana $n = 2$ .

$- \frac{{(1 - x^{2})}^{3} (- 3 {(1 - x^{2})}^{\frac{1}{2}} x + 3 (2 {(1 - x^{2})}^{\frac{1}{2}} x + \frac{x^{2}}{2 {(1 - x^{2})}^{\frac{1}{2}}} (- (2 x)))) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.31

Gabungkan pecahan.

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Langkah 4.31.1

Kalikan $2$ dengan $- 1$ .

$- \frac{{(1 - x^{2})}^{3} (- 3 {(1 - x^{2})}^{\frac{1}{2}} x + 3 (2 {(1 - x^{2})}^{\frac{1}{2}} x + \frac{x^{2}}{2 {(1 - x^{2})}^{\frac{1}{2}}} (- 2 x))) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.31.2

Gabungkan $- 2$ dan $\frac{x^{2}}{2 {(1 - x^{2})}^{\frac{1}{2}}}$ .

$- \frac{{(1 - x^{2})}^{3} (- 3 {(1 - x^{2})}^{\frac{1}{2}} x + 3 (2 {(1 - x^{2})}^{\frac{1}{2}} x + \frac{- 2 x^{2}}{2 {(1 - x^{2})}^{\frac{1}{2}}} x)) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.31.3

Gabungkan $\frac{- 2 x^{2}}{2 {(1 - x^{2})}^{\frac{1}{2}}}$ dan $x$ .

$- \frac{{(1 - x^{2})}^{3} (- 3 {(1 - x^{2})}^{\frac{1}{2}} x + 3 (2 {(1 - x^{2})}^{\frac{1}{2}} x + \frac{- 2 x^{2} x}{2 {(1 - x^{2})}^{\frac{1}{2}}})) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.32

Naikkan $x$ menjadi pangkat $1$ .

$- \frac{{(1 - x^{2})}^{3} (- 3 {(1 - x^{2})}^{\frac{1}{2}} x + 3 (2 {(1 - x^{2})}^{\frac{1}{2}} x + \frac{- 2 (x^{1} x^{2})}{2 {(1 - x^{2})}^{\frac{1}{2}}})) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.33

Gunakan kaidah pangkat $a^{m} a^{n} = a^{m + n}$ untuk menggabungkan pangkat.

$- \frac{{(1 - x^{2})}^{3} (- 3 {(1 - x^{2})}^{\frac{1}{2}} x + 3 (2 {(1 - x^{2})}^{\frac{1}{2}} x + \frac{- 2 x^{1 + 2}}{2 {(1 - x^{2})}^{\frac{1}{2}}})) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.34

Tambahkan $1$ dan $2$ .

$- \frac{{(1 - x^{2})}^{3} (- 3 {(1 - x^{2})}^{\frac{1}{2}} x + 3 (2 {(1 - x^{2})}^{\frac{1}{2}} x + \frac{- 2 x^{3}}{2 {(1 - x^{2})}^{\frac{1}{2}}})) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.35

Faktorkan $2$ dari $- 2 x^{3}$ .

$- \frac{{(1 - x^{2})}^{3} (- 3 {(1 - x^{2})}^{\frac{1}{2}} x + 3 (2 {(1 - x^{2})}^{\frac{1}{2}} x + \frac{2 (- x^{3})}{2 {(1 - x^{2})}^{\frac{1}{2}}})) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.36

Batalkan faktor persekutuan.

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Langkah 4.36.1

Faktorkan $2$ dari $2 {(1 - x^{2})}^{\frac{1}{2}}$ .

$- \frac{{(1 - x^{2})}^{3} (- 3 {(1 - x^{2})}^{\frac{1}{2}} x + 3 (2 {(1 - x^{2})}^{\frac{1}{2}} x + \frac{2 (- x^{3})}{2 ({(1 - x^{2})}^{\frac{1}{2}})})) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.36.2

Batalkan faktor persekutuan.

Langkah 4.36.3

Tulis kembali pernyataannya.

$- \frac{{(1 - x^{2})}^{3} (- 3 {(1 - x^{2})}^{\frac{1}{2}} x + 3 (2 {(1 - x^{2})}^{\frac{1}{2}} x + \frac{- x^{3}}{{(1 - x^{2})}^{\frac{1}{2}}})) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.37

Pindahkan tanda negatif di depan pecahan.

$- \frac{{(1 - x^{2})}^{3} (- 3 {(1 - x^{2})}^{\frac{1}{2}} x + 3 (2 {(1 - x^{2})}^{\frac{1}{2}} x - \frac{x^{3}}{{(1 - x^{2})}^{\frac{1}{2}}})) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.38

Susun kembali $1$ dan $- x^{2}$ .

$- \frac{{(1 - x^{2})}^{3} (- 3 {(1 - x^{2})}^{\frac{1}{2}} x + 3 (2 x {(- x^{2} + 1)}^{\frac{1}{2}} - \frac{x^{3}}{{(- x^{2} + 1)}^{\frac{1}{2}}})) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.39

Untuk menuliskan $2 x {(- x^{2} + 1)}^{\frac{1}{2}}$ sebagai pecahan dengan penyebut umum, kalikan dengan $\frac{{(- x^{2} + 1)}^{\frac{1}{2}}}{{(- x^{2} + 1)}^{\frac{1}{2}}}$ .

$- \frac{{(1 - x^{2})}^{3} (- 3 {(1 - x^{2})}^{\frac{1}{2}} x + 3 (\frac{2 x {(- x^{2} + 1)}^{\frac{1}{2}} {(- x^{2} + 1)}^{\frac{1}{2}}}{{(- x^{2} + 1)}^{\frac{1}{2}}} - \frac{x^{3}}{{(- x^{2} + 1)}^{\frac{1}{2}}})) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.40

Gabungkan pembilang dari penyebut persekutuan.

$- \frac{{(1 - x^{2})}^{3} (- 3 {(1 - x^{2})}^{\frac{1}{2}} x + 3 \frac{2 x {(- x^{2} + 1)}^{\frac{1}{2}} {(- x^{2} + 1)}^{\frac{1}{2}} - x^{3}}{{(- x^{2} + 1)}^{\frac{1}{2}}}) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.41

Kalikan ${(- x^{2} + 1)}^{\frac{1}{2}}$ dengan ${(- x^{2} + 1)}^{\frac{1}{2}}$ dengan menambahkan eksponennya.

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Langkah 4.41.1

Pindahkan ${(- x^{2} + 1)}^{\frac{1}{2}}$ .

$- \frac{{(1 - x^{2})}^{3} (- 3 {(1 - x^{2})}^{\frac{1}{2}} x + 3 \frac{2 x ({(- x^{2} + 1)}^{\frac{1}{2}} {(- x^{2} + 1)}^{\frac{1}{2}}) - x^{3}}{{(- x^{2} + 1)}^{\frac{1}{2}}}) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.41.2

Gunakan kaidah pangkat $a^{m} a^{n} = a^{m + n}$ untuk menggabungkan pangkat.

$- \frac{{(1 - x^{2})}^{3} (- 3 {(1 - x^{2})}^{\frac{1}{2}} x + 3 \frac{2 x {(- x^{2} + 1)}^{\frac{1}{2} + \frac{1}{2}} - x^{3}}{{(- x^{2} + 1)}^{\frac{1}{2}}}) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.41.3

Gabungkan pembilang dari penyebut persekutuan.

$- \frac{{(1 - x^{2})}^{3} (- 3 {(1 - x^{2})}^{\frac{1}{2}} x + 3 \frac{2 x {(- x^{2} + 1)}^{\frac{1 + 1}{2}} - x^{3}}{{(- x^{2} + 1)}^{\frac{1}{2}}}) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.41.4

Tambahkan $1$ dan $1$ .

$- \frac{{(1 - x^{2})}^{3} (- 3 {(1 - x^{2})}^{\frac{1}{2}} x + 3 \frac{2 x {(- x^{2} + 1)}^{\frac{2}{2}} - x^{3}}{{(- x^{2} + 1)}^{\frac{1}{2}}}) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.41.5

Bagilah $2$ dengan $2$ .

$- \frac{{(1 - x^{2})}^{3} (- 3 {(1 - x^{2})}^{\frac{1}{2}} x + 3 \frac{2 x {(- x^{2} + 1)}^{1} - x^{3}}{{(- x^{2} + 1)}^{\frac{1}{2}}}) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.42

Sederhanakan $2 x {(- x^{2} + 1)}^{1}$ .

$- \frac{{(1 - x^{2})}^{3} (- 3 {(1 - x^{2})}^{\frac{1}{2}} x + 3 \frac{2 x (- x^{2} + 1) - x^{3}}{{(- x^{2} + 1)}^{\frac{1}{2}}}) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.43

Gabungkan $3$ dan $\frac{2 x (- x^{2} + 1) - x^{3}}{{(- x^{2} + 1)}^{\frac{1}{2}}}$ .

$- \frac{{(1 - x^{2})}^{3} (- 3 {(1 - x^{2})}^{\frac{1}{2}} x + \frac{3 (2 x (- x^{2} + 1) - x^{3})}{{(- x^{2} + 1)}^{\frac{1}{2}}}) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.44

Untuk menuliskan $- 3 {(1 - x^{2})}^{\frac{1}{2}} x$ sebagai pecahan dengan penyebut umum, kalikan dengan $\frac{{(- x^{2} + 1)}^{\frac{1}{2}}}{{(- x^{2} + 1)}^{\frac{1}{2}}}$ .

$- \frac{{(1 - x^{2})}^{3} (- 3 {(1 - x^{2})}^{\frac{1}{2}} x \cdot \frac{{(- x^{2} + 1)}^{\frac{1}{2}}}{{(- x^{2} + 1)}^{\frac{1}{2}}} + \frac{3 (2 x (- x^{2} + 1) - x^{3})}{{(- x^{2} + 1)}^{\frac{1}{2}}}) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.45

Gabungkan $- 3 {(1 - x^{2})}^{\frac{1}{2}} x$ dan $\frac{{(- x^{2} + 1)}^{\frac{1}{2}}}{{(- x^{2} + 1)}^{\frac{1}{2}}}$ .

$- \frac{{(1 - x^{2})}^{3} (\frac{- 3 {(1 - x^{2})}^{\frac{1}{2}} x {(- x^{2} + 1)}^{\frac{1}{2}}}{{(- x^{2} + 1)}^{\frac{1}{2}}} + \frac{3 (2 x (- x^{2} + 1) - x^{3})}{{(- x^{2} + 1)}^{\frac{1}{2}}}) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.46

Gabungkan pembilang dari penyebut persekutuan.

$- \frac{{(1 - x^{2})}^{3} \frac{- 3 {(1 - x^{2})}^{\frac{1}{2}} x {(- x^{2} + 1)}^{\frac{1}{2}} + 3 (2 x (- x^{2} + 1) - x^{3})}{{(- x^{2} + 1)}^{\frac{1}{2}}} - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.47

Susun kembali suku-suku.

$- \frac{{(1 - x^{2})}^{3} \frac{- 3 {(- x^{2} + 1)}^{\frac{1}{2}} x {(- x^{2} + 1)}^{\frac{1}{2}} + 3 (2 x (- x^{2} + 1) - x^{3})}{{(- x^{2} + 1)}^{\frac{1}{2}}} - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.48

Kalikan ${(- x^{2} + 1)}^{\frac{1}{2}}$ dengan ${(- x^{2} + 1)}^{\frac{1}{2}}$ dengan menambahkan eksponennya.

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Langkah 4.48.1

Pindahkan ${(- x^{2} + 1)}^{\frac{1}{2}}$ .

$- \frac{{(1 - x^{2})}^{3} \frac{- 3 ({(- x^{2} + 1)}^{\frac{1}{2}} {(- x^{2} + 1)}^{\frac{1}{2}}) x + 3 (2 x (- x^{2} + 1) - x^{3})}{{(- x^{2} + 1)}^{\frac{1}{2}}} - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.48.2

Gunakan kaidah pangkat $a^{m} a^{n} = a^{m + n}$ untuk menggabungkan pangkat.

$- \frac{{(1 - x^{2})}^{3} \frac{- 3 {(- x^{2} + 1)}^{\frac{1}{2} + \frac{1}{2}} x + 3 (2 x (- x^{2} + 1) - x^{3})}{{(- x^{2} + 1)}^{\frac{1}{2}}} - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.48.3

Gabungkan pembilang dari penyebut persekutuan.

$- \frac{{(1 - x^{2})}^{3} \frac{- 3 {(- x^{2} + 1)}^{\frac{1 + 1}{2}} x + 3 (2 x (- x^{2} + 1) - x^{3})}{{(- x^{2} + 1)}^{\frac{1}{2}}} - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.48.4

Tambahkan $1$ dan $1$ .

$- \frac{{(1 - x^{2})}^{3} \frac{- 3 {(- x^{2} + 1)}^{\frac{2}{2}} x + 3 (2 x (- x^{2} + 1) - x^{3})}{{(- x^{2} + 1)}^{\frac{1}{2}}} - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.48.5

Bagilah $2$ dengan $2$ .

$- \frac{{(1 - x^{2})}^{3} \frac{- 3 {(- x^{2} + 1)}^{1} x + 3 (2 x (- x^{2} + 1) - x^{3})}{{(- x^{2} + 1)}^{\frac{1}{2}}} - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.49

Sederhanakan $- 3 {(- x^{2} + 1)}^{1} x$ .

$- \frac{{(1 - x^{2})}^{3} \frac{- 3 (- x^{2} + 1) x + 3 (2 x (- x^{2} + 1) - x^{3})}{{(- x^{2} + 1)}^{\frac{1}{2}}} - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.50

Gabungkan ${(1 - x^{2})}^{3}$ dan $\frac{- 3 (- x^{2} + 1) x + 3 (2 x (- x^{2} + 1) - x^{3})}{{(- x^{2} + 1)}^{\frac{1}{2}}}$ .

$- \frac{\frac{{(1 - x^{2})}^{3} (- 3 (- x^{2} + 1) x + 3 (2 x (- x^{2} + 1) - x^{3}))}{{(- x^{2} + 1)}^{\frac{1}{2}}} - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.51

Susun kembali suku-suku.

$- \frac{\frac{{(- x^{2} + 1)}^{3} (- 3 (- x^{2} + 1) x + 3 (2 x (- x^{2} + 1) - x^{3}))}{{(- x^{2} + 1)}^{\frac{1}{2}}} - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.52

Faktorkan ${(- x^{2} + 1)}^{\frac{1}{2}}$ dari ${(- x^{2} + 1)}^{3} (- 3 (- x^{2} + 1) x + 3 (2 x (- x^{2} + 1) - x^{3}))$ .

$- \frac{\frac{{(- x^{2} + 1)}^{\frac{1}{2}} ({(- x^{2} + 1)}^{\frac{5}{2}} (- 3 (- x^{2} + 1) x + 3 (2 x (- x^{2} + 1) - x^{3})))}{{(- x^{2} + 1)}^{\frac{1}{2}}} - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.53

Batalkan faktor persekutuan.

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Langkah 4.53.1

Kalikan dengan $1$ .

$- \frac{\frac{{(- x^{2} + 1)}^{\frac{1}{2}} ({(- x^{2} + 1)}^{\frac{5}{2}} (- 3 (- x^{2} + 1) x + 3 (2 x (- x^{2} + 1) - x^{3})))}{{(- x^{2} + 1)}^{\frac{1}{2}} \cdot 1} - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.53.2

Batalkan faktor persekutuan.

Langkah 4.53.3

Tulis kembali pernyataannya.

$- \frac{\frac{{(- x^{2} + 1)}^{\frac{5}{2}} (- 3 (- x^{2} + 1) x + 3 (2 x (- x^{2} + 1) - x^{3}))}{1} - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.53.4

Bagilah ${(- x^{2} + 1)}^{\frac{5}{2}} (- 3 (- x^{2} + 1) x + 3 (2 x (- x^{2} + 1) - x^{3}))$ dengan $1$ .

$- \frac{{(- x^{2} + 1)}^{\frac{5}{2}} (- 3 (- x^{2} + 1) x + 3 (2 x (- x^{2} + 1) - x^{3})) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) \frac{d}{d x} [{(1 - x^{2})}^{3}]}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.54

Diferensialkan menggunakan kaidah rantai, yang menyatakan bahwa $\frac{d}{d x} [f (g (x))]$ adalah $f' (g (x)) g' (x)$ di mana $f (x) = x^{3}$ dan $g (x) = 1 - x^{2}$ .

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Langkah 4.54.1

Untuk menerapkan Kaidah Rantai, atur $u_{3}$ sebagai $1 - x^{2}$ .

$- \frac{{(- x^{2} + 1)}^{\frac{5}{2}} (- 3 (- x^{2} + 1) x + 3 (2 x (- x^{2} + 1) - x^{3})) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) (\frac{d}{d u_{3}} [{u_{3}}^{3}] \frac{d}{d x} [1 - x^{2}])}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.54.2

Diferensialkan menggunakan Kaidah Pangkat yang menyatakan bahwa $\frac{d}{d u_{3}} [{u_{3}}^{n}]$ adalah $n {u_{3}}^{n - 1}$ di mana $n = 3$ .

$- \frac{{(- x^{2} + 1)}^{\frac{5}{2}} (- 3 (- x^{2} + 1) x + 3 (2 x (- x^{2} + 1) - x^{3})) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) (3 {u_{3}}^{2} \frac{d}{d x} [1 - x^{2}])}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.54.3

Ganti semua kemunculan $u_{3}$ dengan $1 - x^{2}$ .

$- \frac{{(- x^{2} + 1)}^{\frac{5}{2}} (- 3 (- x^{2} + 1) x + 3 (2 x (- x^{2} + 1) - x^{3})) - ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) (3 {(1 - x^{2})}^{2} \frac{d}{d x} [1 - x^{2}])}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.55

Diferensialkan.

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Langkah 4.55.1

Kalikan $3$ dengan $- 1$ .

$- \frac{{(- x^{2} + 1)}^{\frac{5}{2}} (- 3 (- x^{2} + 1) x + 3 (2 x (- x^{2} + 1) - x^{3})) - 3 ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) ({(1 - x^{2})}^{2} \frac{d}{d x} [1 - x^{2}])}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.55.2

Menurut Kaidah Penjumlahan, turunan dari $1 - x^{2}$ terhadap $x$ adalah $\frac{d}{d x} [1] + \frac{d}{d x} [- x^{2}]$ .

$- \frac{{(- x^{2} + 1)}^{\frac{5}{2}} (- 3 (- x^{2} + 1) x + 3 (2 x (- x^{2} + 1) - x^{3})) - 3 ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) ({(1 - x^{2})}^{2} (\frac{d}{d x} [1] + \frac{d}{d x} [- x^{2}]))}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.55.3

Karena $1$ konstan terhadap $x$ , turunan dari $1$ terhadap $x$ adalah $0$ .

$- \frac{{(- x^{2} + 1)}^{\frac{5}{2}} (- 3 (- x^{2} + 1) x + 3 (2 x (- x^{2} + 1) - x^{3})) - 3 ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) ({(1 - x^{2})}^{2} (0 + \frac{d}{d x} [- x^{2}]))}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.55.4

Tambahkan $0$ dan $\frac{d}{d x} [- x^{2}]$ .

$- \frac{{(- x^{2} + 1)}^{\frac{5}{2}} (- 3 (- x^{2} + 1) x + 3 (2 x (- x^{2} + 1) - x^{3})) - 3 ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) ({(1 - x^{2})}^{2} \frac{d}{d x} [- x^{2}])}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.55.5

Karena $- 1$ konstan terhadap $x$ , turunan dari $- x^{2}$ terhadap $x$ adalah $- \frac{d}{d x} [x^{2}]$ .

$- \frac{{(- x^{2} + 1)}^{\frac{5}{2}} (- 3 (- x^{2} + 1) x + 3 (2 x (- x^{2} + 1) - x^{3})) - 3 ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) ({(1 - x^{2})}^{2} (- \frac{d}{d x} [x^{2}]))}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.55.6

Kalikan $- 1$ dengan $- 3$ .

$- \frac{{(- x^{2} + 1)}^{\frac{5}{2}} (- 3 (- x^{2} + 1) x + 3 (2 x (- x^{2} + 1) - x^{3})) + 3 ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) ({(1 - x^{2})}^{2} (\frac{d}{d x} [x^{2}]))}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.55.7

Diferensialkan menggunakan Kaidah Pangkat yang menyatakan bahwa $\frac{d}{d x} [x^{n}]$ adalah $n x^{n - 1}$ di mana $n = 2$ .

$- \frac{{(- x^{2} + 1)}^{\frac{5}{2}} (- 3 (- x^{2} + 1) x + 3 (2 x (- x^{2} + 1) - x^{3})) + 3 ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) ({(1 - x^{2})}^{2} (2 x))}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.55.8

Sederhanakan pernyataannya.

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Langkah 4.55.8.1

Pindahkan $2$ ke sebelah kiri ${(1 - x^{2})}^{2}$ .

$- \frac{{(- x^{2} + 1)}^{\frac{5}{2}} (- 3 (- x^{2} + 1) x + 3 (2 x (- x^{2} + 1) - x^{3})) + 3 ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) (2 \cdot {(1 - x^{2})}^{2} x)}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.55.8.2

Kalikan $2$ dengan $3$ .

$- \frac{{(- x^{2} + 1)}^{\frac{5}{2}} (- 3 (- x^{2} + 1) x + 3 (2 x (- x^{2} + 1) - x^{3})) + 6 ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) ({(1 - x^{2})}^{2} x)}{{(1 - x^{2})}^{6}} + \frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}} \frac{d}{d x} [- 1]$

Langkah 4.55.9

Karena $- 1$ konstan terhadap $x$ , turunan dari $- 1$ terhadap $x$ adalah $0$ .

Langkah 4.55.10

Sederhanakan pernyataannya.

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Langkah 4.55.10.1

Kalikan $\frac{{(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}}{{(1 - x^{2})}^{3}}$ dengan $0$ .

Langkah 4.55.10.2

Tambahkan $- \frac{{(- x^{2} + 1)}^{\frac{5}{2}} (- 3 (- x^{2} + 1) x + 3 (2 x (- x^{2} + 1) - x^{3})) + 6 ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) ({(1 - x^{2})}^{2} x)}{{(1 - x^{2})}^{6}}$ dan $0$ .

Langkah 4.56

Sederhanakan.

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Langkah 4.56.1

Terapkan sifat distributif.

$- \frac{{(- x^{2} + 1)}^{\frac{5}{2}} ((- 3 (- x^{2}) - 3 \cdot 1) x + 3 (2 x (- x^{2} + 1) - x^{3})) + 6 ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) ({(1 - x^{2})}^{2} x)}{{(1 - x^{2})}^{6}}$

Langkah 4.56.2

Terapkan sifat distributif.

$- \frac{{(- x^{2} + 1)}^{\frac{5}{2}} (- 3 (- x^{2}) x - 3 \cdot 1 x + 3 (2 x (- x^{2} + 1) - x^{3})) + 6 ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) ({(1 - x^{2})}^{2} x)}{{(1 - x^{2})}^{6}}$

Langkah 4.56.3

Terapkan sifat distributif.

$- \frac{{(- x^{2} + 1)}^{\frac{5}{2}} (- 3 (- x^{2}) x - 3 \cdot 1 x + 3 (2 x (- x^{2}) + 2 x \cdot 1 - x^{3})) + 6 ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) ({(1 - x^{2})}^{2} x)}{{(1 - x^{2})}^{6}}$

Langkah 4.56.4

Terapkan sifat distributif.

$- \frac{{(- x^{2} + 1)}^{\frac{5}{2}} (- 3 (- x^{2}) x - 3 \cdot 1 x + 3 (2 x (- x^{2})) + 3 (2 x \cdot 1) + 3 (- x^{3})) + 6 ({(1 - x^{2})}^{\frac{3}{2}} + 3 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) ({(1 - x^{2})}^{2} x)}{{(1 - x^{2})}^{6}}$

Langkah 4.56.5

Terapkan sifat distributif.

$- \frac{{(- x^{2} + 1)}^{\frac{5}{2}} (- 3 (- x^{2}) x - 3 \cdot 1 x + 3 (2 x (- x^{2})) + 3 (2 x \cdot 1) + 3 (- x^{3})) + (6 {(1 - x^{2})}^{\frac{3}{2}} + 6 (3 {(1 - x^{2})}^{\frac{1}{2}} x^{2})) ({(1 - x^{2})}^{2} x)}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6

Sederhanakan pembilangnya.

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Langkah 4.56.6.1

Sederhanakan setiap suku.

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Langkah 4.56.6.1.1

Kalikan $x^{2}$ dengan $x$ dengan menambahkan eksponennya.

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Langkah 4.56.6.1.1.1

Pindahkan $x$ .

$- \frac{{(- x^{2} + 1)}^{\frac{5}{2}} (- 3 (- (x \cdot x^{2})) - 3 \cdot 1 x + 3 (2 x (- x^{2})) + 3 (2 x \cdot 1) + 3 (- x^{3})) + (6 {(1 - x^{2})}^{\frac{3}{2}} + 6 (3 {(1 - x^{2})}^{\frac{1}{2}} x^{2})) ({(1 - x^{2})}^{2} x)}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.1.1.2

Kalikan $x$ dengan $x^{2}$ .

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Langkah 4.56.6.1.1.2.1

Naikkan $x$ menjadi pangkat $1$ .

$- \frac{{(- x^{2} + 1)}^{\frac{5}{2}} (- 3 (- (x^{1} x^{2})) - 3 \cdot 1 x + 3 (2 x (- x^{2})) + 3 (2 x \cdot 1) + 3 (- x^{3})) + (6 {(1 - x^{2})}^{\frac{3}{2}} + 6 (3 {(1 - x^{2})}^{\frac{1}{2}} x^{2})) ({(1 - x^{2})}^{2} x)}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.1.1.2.2

Gunakan kaidah pangkat $a^{m} a^{n} = a^{m + n}$ untuk menggabungkan pangkat.

$- \frac{{(- x^{2} + 1)}^{\frac{5}{2}} (- 3 (- x^{1 + 2}) - 3 \cdot 1 x + 3 (2 x (- x^{2})) + 3 (2 x \cdot 1) + 3 (- x^{3})) + (6 {(1 - x^{2})}^{\frac{3}{2}} + 6 (3 {(1 - x^{2})}^{\frac{1}{2}} x^{2})) ({(1 - x^{2})}^{2} x)}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.1.1.3

Tambahkan $1$ dan $2$ .

$- \frac{{(- x^{2} + 1)}^{\frac{5}{2}} (- 3 (- x^{3}) - 3 \cdot 1 x + 3 (2 x (- x^{2})) + 3 (2 x \cdot 1) + 3 (- x^{3})) + (6 {(1 - x^{2})}^{\frac{3}{2}} + 6 (3 {(1 - x^{2})}^{\frac{1}{2}} x^{2})) ({(1 - x^{2})}^{2} x)}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.1.2

Kalikan $- 1$ dengan $- 3$ .

$- \frac{{(- x^{2} + 1)}^{\frac{5}{2}} (3 x^{3} - 3 \cdot 1 x + 3 (2 x (- x^{2})) + 3 (2 x \cdot 1) + 3 (- x^{3})) + (6 {(1 - x^{2})}^{\frac{3}{2}} + 6 (3 {(1 - x^{2})}^{\frac{1}{2}} x^{2})) ({(1 - x^{2})}^{2} x)}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.1.3

Kalikan $- 3$ dengan $1$ .

$- \frac{{(- x^{2} + 1)}^{\frac{5}{2}} (3 x^{3} - 3 x + 3 (2 x (- x^{2})) + 3 (2 x \cdot 1) + 3 (- x^{3})) + (6 {(1 - x^{2})}^{\frac{3}{2}} + 6 (3 {(1 - x^{2})}^{\frac{1}{2}} x^{2})) ({(1 - x^{2})}^{2} x)}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.1.4

Kalikan $x$ dengan $x^{2}$ dengan menambahkan eksponennya.

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Langkah 4.56.6.1.4.1

Pindahkan $x^{2}$ .

$- \frac{{(- x^{2} + 1)}^{\frac{5}{2}} (3 x^{3} - 3 x + 3 (2 (x^{2} x) \cdot - 1) + 3 (2 x \cdot 1) + 3 (- x^{3})) + (6 {(1 - x^{2})}^{\frac{3}{2}} + 6 (3 {(1 - x^{2})}^{\frac{1}{2}} x^{2})) ({(1 - x^{2})}^{2} x)}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.1.4.2

Kalikan $x^{2}$ dengan $x$ .

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Langkah 4.56.6.1.4.2.1

Naikkan $x$ menjadi pangkat $1$ .

$- \frac{{(- x^{2} + 1)}^{\frac{5}{2}} (3 x^{3} - 3 x + 3 (2 (x^{2} x^{1}) \cdot - 1) + 3 (2 x \cdot 1) + 3 (- x^{3})) + (6 {(1 - x^{2})}^{\frac{3}{2}} + 6 (3 {(1 - x^{2})}^{\frac{1}{2}} x^{2})) ({(1 - x^{2})}^{2} x)}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.1.4.2.2

Gunakan kaidah pangkat $a^{m} a^{n} = a^{m + n}$ untuk menggabungkan pangkat.

$- \frac{{(- x^{2} + 1)}^{\frac{5}{2}} (3 x^{3} - 3 x + 3 (2 x^{2 + 1} \cdot - 1) + 3 (2 x \cdot 1) + 3 (- x^{3})) + (6 {(1 - x^{2})}^{\frac{3}{2}} + 6 (3 {(1 - x^{2})}^{\frac{1}{2}} x^{2})) ({(1 - x^{2})}^{2} x)}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.1.4.3

Tambahkan $2$ dan $1$ .

$- \frac{{(- x^{2} + 1)}^{\frac{5}{2}} (3 x^{3} - 3 x + 3 (2 x^{3} \cdot - 1) + 3 (2 x \cdot 1) + 3 (- x^{3})) + (6 {(1 - x^{2})}^{\frac{3}{2}} + 6 (3 {(1 - x^{2})}^{\frac{1}{2}} x^{2})) ({(1 - x^{2})}^{2} x)}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.1.5

Kalikan $- 1$ dengan $2$ .

$- \frac{{(- x^{2} + 1)}^{\frac{5}{2}} (3 x^{3} - 3 x + 3 (- 2 x^{3}) + 3 (2 x \cdot 1) + 3 (- x^{3})) + (6 {(1 - x^{2})}^{\frac{3}{2}} + 6 (3 {(1 - x^{2})}^{\frac{1}{2}} x^{2})) ({(1 - x^{2})}^{2} x)}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.1.6

Kalikan $- 2$ dengan $3$ .

$- \frac{{(- x^{2} + 1)}^{\frac{5}{2}} (3 x^{3} - 3 x - 6 x^{3} + 3 (2 x \cdot 1) + 3 (- x^{3})) + (6 {(1 - x^{2})}^{\frac{3}{2}} + 6 (3 {(1 - x^{2})}^{\frac{1}{2}} x^{2})) ({(1 - x^{2})}^{2} x)}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.1.7

Kalikan $2$ dengan $1$ .

$- \frac{{(- x^{2} + 1)}^{\frac{5}{2}} (3 x^{3} - 3 x - 6 x^{3} + 3 (2 x) + 3 (- x^{3})) + (6 {(1 - x^{2})}^{\frac{3}{2}} + 6 (3 {(1 - x^{2})}^{\frac{1}{2}} x^{2})) ({(1 - x^{2})}^{2} x)}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.1.8

Kalikan $2$ dengan $3$ .

$- \frac{{(- x^{2} + 1)}^{\frac{5}{2}} (3 x^{3} - 3 x - 6 x^{3} + 6 x + 3 (- x^{3})) + (6 {(1 - x^{2})}^{\frac{3}{2}} + 6 (3 {(1 - x^{2})}^{\frac{1}{2}} x^{2})) ({(1 - x^{2})}^{2} x)}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.1.9

Kalikan $- 1$ dengan $3$ .

$- \frac{{(- x^{2} + 1)}^{\frac{5}{2}} (3 x^{3} - 3 x - 6 x^{3} + 6 x - 3 x^{3}) + (6 {(1 - x^{2})}^{\frac{3}{2}} + 6 (3 {(1 - x^{2})}^{\frac{1}{2}} x^{2})) ({(1 - x^{2})}^{2} x)}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.2

Gabungkan suku balikan dalam $3 x^{3} - 3 x - 6 x^{3} + 6 x - 3 x^{3}$ .

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Langkah 4.56.6.2.1

Kurangi $3 x^{3}$ dengan $3 x^{3}$ .

$- \frac{{(- x^{2} + 1)}^{\frac{5}{2}} (- 3 x - 6 x^{3} + 6 x + 0) + (6 {(1 - x^{2})}^{\frac{3}{2}} + 6 (3 {(1 - x^{2})}^{\frac{1}{2}} x^{2})) ({(1 - x^{2})}^{2} x)}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.2.2

Tambahkan $- 3 x - 6 x^{3} + 6 x$ dan $0$ .

$- \frac{{(- x^{2} + 1)}^{\frac{5}{2}} (- 3 x - 6 x^{3} + 6 x) + (6 {(1 - x^{2})}^{\frac{3}{2}} + 6 (3 {(1 - x^{2})}^{\frac{1}{2}} x^{2})) ({(1 - x^{2})}^{2} x)}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.3

Tambahkan $- 3 x$ dan $6 x$ .

$- \frac{{(- x^{2} + 1)}^{\frac{5}{2}} (- 6 x^{3} + 3 x) + (6 {(1 - x^{2})}^{\frac{3}{2}} + 6 (3 {(1 - x^{2})}^{\frac{1}{2}} x^{2})) ({(1 - x^{2})}^{2} x)}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.4

Terapkan sifat distributif.

$- \frac{{(- x^{2} + 1)}^{\frac{5}{2}} (- 6 x^{3}) + {(- x^{2} + 1)}^{\frac{5}{2}} (3 x) + (6 {(1 - x^{2})}^{\frac{3}{2}} + 6 (3 {(1 - x^{2})}^{\frac{1}{2}} x^{2})) ({(1 - x^{2})}^{2} x)}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.5

Tulis kembali menggunakan sifat komutatif dari perkalian.

$- \frac{- 6 {(- x^{2} + 1)}^{\frac{5}{2}} x^{3} + {(- x^{2} + 1)}^{\frac{5}{2}} (3 x) + (6 {(1 - x^{2})}^{\frac{3}{2}} + 6 (3 {(1 - x^{2})}^{\frac{1}{2}} x^{2})) ({(1 - x^{2})}^{2} x)}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.6

Tulis kembali menggunakan sifat komutatif dari perkalian.

$- \frac{- 6 {(- x^{2} + 1)}^{\frac{5}{2}} x^{3} + 3 {(- x^{2} + 1)}^{\frac{5}{2}} x + (6 {(1 - x^{2})}^{\frac{3}{2}} + 6 (3 {(1 - x^{2})}^{\frac{1}{2}} x^{2})) ({(1 - x^{2})}^{2} x)}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.7

Kalikan $3$ dengan $6$ .

$- \frac{- 6 {(- x^{2} + 1)}^{\frac{5}{2}} x^{3} + 3 {(- x^{2} + 1)}^{\frac{5}{2}} x + (6 {(1 - x^{2})}^{\frac{3}{2}} + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) ({(1 - x^{2})}^{2} x)}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.8

Tulis kembali ${(1 - x^{2})}^{2}$ sebagai $(1 - x^{2}) (1 - x^{2})$ .

$- \frac{- 6 {(- x^{2} + 1)}^{\frac{5}{2}} x^{3} + 3 {(- x^{2} + 1)}^{\frac{5}{2}} x + (6 {(1 - x^{2})}^{\frac{3}{2}} + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) ((1 - x^{2}) (1 - x^{2}) x)}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.9

Perluas $(1 - x^{2}) (1 - x^{2})$ menggunakan Metode FOIL.

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Langkah 4.56.6.9.1

Terapkan sifat distributif.

$- \frac{- 6 {(- x^{2} + 1)}^{\frac{5}{2}} x^{3} + 3 {(- x^{2} + 1)}^{\frac{5}{2}} x + (6 {(1 - x^{2})}^{\frac{3}{2}} + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) ((1 (1 - x^{2}) - x^{2} (1 - x^{2})) x)}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.9.2

Terapkan sifat distributif.

$- \frac{- 6 {(- x^{2} + 1)}^{\frac{5}{2}} x^{3} + 3 {(- x^{2} + 1)}^{\frac{5}{2}} x + (6 {(1 - x^{2})}^{\frac{3}{2}} + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) ((1 \cdot 1 + 1 (- x^{2}) - x^{2} (1 - x^{2})) x)}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.9.3

Terapkan sifat distributif.

Langkah 4.56.6.10

Sederhanakan dan gabungkan suku-suku sejenis.

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Langkah 4.56.6.10.1

Sederhanakan setiap suku.

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Langkah 4.56.6.10.1.1

Kalikan $1$ dengan $1$ .

$- \frac{- 6 {(- x^{2} + 1)}^{\frac{5}{2}} x^{3} + 3 {(- x^{2} + 1)}^{\frac{5}{2}} x + (6 {(1 - x^{2})}^{\frac{3}{2}} + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) ((1 + 1 (- x^{2}) - x^{2} \cdot 1 - x^{2} (- x^{2})) x)}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.10.1.2

Kalikan $- x^{2}$ dengan $1$ .

$- \frac{- 6 {(- x^{2} + 1)}^{\frac{5}{2}} x^{3} + 3 {(- x^{2} + 1)}^{\frac{5}{2}} x + (6 {(1 - x^{2})}^{\frac{3}{2}} + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) ((1 - x^{2} - x^{2} \cdot 1 - x^{2} (- x^{2})) x)}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.10.1.3

Kalikan $- 1$ dengan $1$ .

$- \frac{- 6 {(- x^{2} + 1)}^{\frac{5}{2}} x^{3} + 3 {(- x^{2} + 1)}^{\frac{5}{2}} x + (6 {(1 - x^{2})}^{\frac{3}{2}} + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) ((1 - x^{2} - x^{2} - x^{2} (- x^{2})) x)}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.10.1.4

Tulis kembali menggunakan sifat komutatif dari perkalian.

$- \frac{- 6 {(- x^{2} + 1)}^{\frac{5}{2}} x^{3} + 3 {(- x^{2} + 1)}^{\frac{5}{2}} x + (6 {(1 - x^{2})}^{\frac{3}{2}} + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) ((1 - x^{2} - x^{2} - 1 \cdot - 1 x^{2} x^{2}) x)}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.10.1.5

Kalikan $x^{2}$ dengan $x^{2}$ dengan menambahkan eksponennya.

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Langkah 4.56.6.10.1.5.1

Pindahkan $x^{2}$ .

Langkah 4.56.6.10.1.5.2

Gunakan kaidah pangkat $a^{m} a^{n} = a^{m + n}$ untuk menggabungkan pangkat.

Langkah 4.56.6.10.1.5.3

Tambahkan $2$ dan $2$ .

Langkah 4.56.6.10.1.6

Kalikan $- 1$ dengan $- 1$ .

$- \frac{- 6 {(- x^{2} + 1)}^{\frac{5}{2}} x^{3} + 3 {(- x^{2} + 1)}^{\frac{5}{2}} x + (6 {(1 - x^{2})}^{\frac{3}{2}} + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) ((1 - x^{2} - x^{2} + 1 x^{4}) x)}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.10.1.7

Kalikan $x^{4}$ dengan $1$ .

$- \frac{- 6 {(- x^{2} + 1)}^{\frac{5}{2}} x^{3} + 3 {(- x^{2} + 1)}^{\frac{5}{2}} x + (6 {(1 - x^{2})}^{\frac{3}{2}} + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) ((1 - x^{2} - x^{2} + x^{4}) x)}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.10.2

Kurangi $x^{2}$ dengan $- x^{2}$ .

$- \frac{- 6 {(- x^{2} + 1)}^{\frac{5}{2}} x^{3} + 3 {(- x^{2} + 1)}^{\frac{5}{2}} x + (6 {(1 - x^{2})}^{\frac{3}{2}} + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) ((1 - 2 x^{2} + x^{4}) x)}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.11

Terapkan sifat distributif.

$- \frac{- 6 {(- x^{2} + 1)}^{\frac{5}{2}} x^{3} + 3 {(- x^{2} + 1)}^{\frac{5}{2}} x + (6 {(1 - x^{2})}^{\frac{3}{2}} + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) (1 x - 2 x^{2} x + x^{4} x)}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.12

Sederhanakan.

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Langkah 4.56.6.12.1

Kalikan $x$ dengan $1$ .

$- \frac{- 6 {(- x^{2} + 1)}^{\frac{5}{2}} x^{3} + 3 {(- x^{2} + 1)}^{\frac{5}{2}} x + (6 {(1 - x^{2})}^{\frac{3}{2}} + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) (x - 2 x^{2} x + x^{4} x)}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.12.2

Kalikan $x^{2}$ dengan $x$ dengan menambahkan eksponennya.

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Langkah 4.56.6.12.2.1

Pindahkan $x$ .

$- \frac{- 6 {(- x^{2} + 1)}^{\frac{5}{2}} x^{3} + 3 {(- x^{2} + 1)}^{\frac{5}{2}} x + (6 {(1 - x^{2})}^{\frac{3}{2}} + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) (x - 2 (x \cdot x^{2}) + x^{4} x)}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.12.2.2

Kalikan $x$ dengan $x^{2}$ .

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Langkah 4.56.6.12.2.2.1

Naikkan $x$ menjadi pangkat $1$ .

$- \frac{- 6 {(- x^{2} + 1)}^{\frac{5}{2}} x^{3} + 3 {(- x^{2} + 1)}^{\frac{5}{2}} x + (6 {(1 - x^{2})}^{\frac{3}{2}} + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) (x - 2 (x^{1} x^{2}) + x^{4} x)}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.12.2.2.2

Gunakan kaidah pangkat $a^{m} a^{n} = a^{m + n}$ untuk menggabungkan pangkat.

$- \frac{- 6 {(- x^{2} + 1)}^{\frac{5}{2}} x^{3} + 3 {(- x^{2} + 1)}^{\frac{5}{2}} x + (6 {(1 - x^{2})}^{\frac{3}{2}} + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) (x - 2 x^{1 + 2} + x^{4} x)}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.12.2.3

Tambahkan $1$ dan $2$ .

$- \frac{- 6 {(- x^{2} + 1)}^{\frac{5}{2}} x^{3} + 3 {(- x^{2} + 1)}^{\frac{5}{2}} x + (6 {(1 - x^{2})}^{\frac{3}{2}} + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) (x - 2 x^{3} + x^{4} x)}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.12.3

Kalikan $x^{4}$ dengan $x$ dengan menambahkan eksponennya.

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Langkah 4.56.6.12.3.1

Kalikan $x^{4}$ dengan $x$ .

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Langkah 4.56.6.12.3.1.1

Naikkan $x$ menjadi pangkat $1$ .

$- \frac{- 6 {(- x^{2} + 1)}^{\frac{5}{2}} x^{3} + 3 {(- x^{2} + 1)}^{\frac{5}{2}} x + (6 {(1 - x^{2})}^{\frac{3}{2}} + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) (x - 2 x^{3} + x^{4} x^{1})}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.12.3.1.2

Gunakan kaidah pangkat $a^{m} a^{n} = a^{m + n}$ untuk menggabungkan pangkat.

$- \frac{- 6 {(- x^{2} + 1)}^{\frac{5}{2}} x^{3} + 3 {(- x^{2} + 1)}^{\frac{5}{2}} x + (6 {(1 - x^{2})}^{\frac{3}{2}} + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) (x - 2 x^{3} + x^{4 + 1})}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.12.3.2

Tambahkan $4$ dan $1$ .

$- \frac{- 6 {(- x^{2} + 1)}^{\frac{5}{2}} x^{3} + 3 {(- x^{2} + 1)}^{\frac{5}{2}} x + (6 {(1 - x^{2})}^{\frac{3}{2}} + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) (x - 2 x^{3} + x^{5})}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.13

Perluas $(6 {(1 - x^{2})}^{\frac{3}{2}} + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) (x - 2 x^{3} + x^{5})$ dengan mengalikan setiap suku dalam pernyataan pertama dengan setiap suku dalam pernyataan kedua.

$- \frac{- 6 {(- x^{2} + 1)}^{\frac{5}{2}} x^{3} + 3 {(- x^{2} + 1)}^{\frac{5}{2}} x + 6 {(1 - x^{2})}^{\frac{3}{2}} x + 6 {(1 - x^{2})}^{\frac{3}{2}} (- 2 x^{3}) + 6 {(1 - x^{2})}^{\frac{3}{2}} x^{5} + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{2} x + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{2} (- 2 x^{3}) + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{2} x^{5}}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.14

Sederhanakan setiap suku.

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Langkah 4.56.6.14.1

Tulis kembali menggunakan sifat komutatif dari perkalian.

$- \frac{- 6 {(- x^{2} + 1)}^{\frac{5}{2}} x^{3} + 3 {(- x^{2} + 1)}^{\frac{5}{2}} x + 6 {(1 - x^{2})}^{\frac{3}{2}} x + 6 \cdot - 2 {(1 - x^{2})}^{\frac{3}{2}} x^{3} + 6 {(1 - x^{2})}^{\frac{3}{2}} x^{5} + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{2} x + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{2} (- 2 x^{3}) + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{2} x^{5}}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.14.2

Kalikan $6$ dengan $- 2$ .

$- \frac{- 6 {(- x^{2} + 1)}^{\frac{5}{2}} x^{3} + 3 {(- x^{2} + 1)}^{\frac{5}{2}} x + 6 {(1 - x^{2})}^{\frac{3}{2}} x - 12 {(1 - x^{2})}^{\frac{3}{2}} x^{3} + 6 {(1 - x^{2})}^{\frac{3}{2}} x^{5} + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{2} x + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{2} (- 2 x^{3}) + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{2} x^{5}}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.14.3

Kalikan $x^{2}$ dengan $x$ dengan menambahkan eksponennya.

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Langkah 4.56.6.14.3.1

Pindahkan $x$ .

$- \frac{- 6 {(- x^{2} + 1)}^{\frac{5}{2}} x^{3} + 3 {(- x^{2} + 1)}^{\frac{5}{2}} x + 6 {(1 - x^{2})}^{\frac{3}{2}} x - 12 {(1 - x^{2})}^{\frac{3}{2}} x^{3} + 6 {(1 - x^{2})}^{\frac{3}{2}} x^{5} + 18 {(1 - x^{2})}^{\frac{1}{2}} (x \cdot x^{2}) + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{2} (- 2 x^{3}) + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{2} x^{5}}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.14.3.2

Kalikan $x$ dengan $x^{2}$ .

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Langkah 4.56.6.14.3.2.1

Naikkan $x$ menjadi pangkat $1$ .

$- \frac{- 6 {(- x^{2} + 1)}^{\frac{5}{2}} x^{3} + 3 {(- x^{2} + 1)}^{\frac{5}{2}} x + 6 {(1 - x^{2})}^{\frac{3}{2}} x - 12 {(1 - x^{2})}^{\frac{3}{2}} x^{3} + 6 {(1 - x^{2})}^{\frac{3}{2}} x^{5} + 18 {(1 - x^{2})}^{\frac{1}{2}} (x^{1} x^{2}) + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{2} (- 2 x^{3}) + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{2} x^{5}}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.14.3.2.2

Gunakan kaidah pangkat $a^{m} a^{n} = a^{m + n}$ untuk menggabungkan pangkat.

$- \frac{- 6 {(- x^{2} + 1)}^{\frac{5}{2}} x^{3} + 3 {(- x^{2} + 1)}^{\frac{5}{2}} x + 6 {(1 - x^{2})}^{\frac{3}{2}} x - 12 {(1 - x^{2})}^{\frac{3}{2}} x^{3} + 6 {(1 - x^{2})}^{\frac{3}{2}} x^{5} + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{1 + 2} + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{2} (- 2 x^{3}) + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{2} x^{5}}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.14.3.3

Tambahkan $1$ dan $2$ .

$- \frac{- 6 {(- x^{2} + 1)}^{\frac{5}{2}} x^{3} + 3 {(- x^{2} + 1)}^{\frac{5}{2}} x + 6 {(1 - x^{2})}^{\frac{3}{2}} x - 12 {(1 - x^{2})}^{\frac{3}{2}} x^{3} + 6 {(1 - x^{2})}^{\frac{3}{2}} x^{5} + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{3} + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{2} (- 2 x^{3}) + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{2} x^{5}}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.14.4

Kalikan $x^{2}$ dengan $x^{3}$ dengan menambahkan eksponennya.

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Langkah 4.56.6.14.4.1

Pindahkan $x^{3}$ .

$- \frac{- 6 {(- x^{2} + 1)}^{\frac{5}{2}} x^{3} + 3 {(- x^{2} + 1)}^{\frac{5}{2}} x + 6 {(1 - x^{2})}^{\frac{3}{2}} x - 12 {(1 - x^{2})}^{\frac{3}{2}} x^{3} + 6 {(1 - x^{2})}^{\frac{3}{2}} x^{5} + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{3} + 18 {(1 - x^{2})}^{\frac{1}{2}} (x^{3} x^{2}) \cdot - 2 + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{2} x^{5}}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.14.4.2

Gunakan kaidah pangkat $a^{m} a^{n} = a^{m + n}$ untuk menggabungkan pangkat.

$- \frac{- 6 {(- x^{2} + 1)}^{\frac{5}{2}} x^{3} + 3 {(- x^{2} + 1)}^{\frac{5}{2}} x + 6 {(1 - x^{2})}^{\frac{3}{2}} x - 12 {(1 - x^{2})}^{\frac{3}{2}} x^{3} + 6 {(1 - x^{2})}^{\frac{3}{2}} x^{5} + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{3} + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{3 + 2} \cdot - 2 + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{2} x^{5}}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.14.4.3

Tambahkan $3$ dan $2$ .

$- \frac{- 6 {(- x^{2} + 1)}^{\frac{5}{2}} x^{3} + 3 {(- x^{2} + 1)}^{\frac{5}{2}} x + 6 {(1 - x^{2})}^{\frac{3}{2}} x - 12 {(1 - x^{2})}^{\frac{3}{2}} x^{3} + 6 {(1 - x^{2})}^{\frac{3}{2}} x^{5} + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{3} + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{5} \cdot - 2 + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{2} x^{5}}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.14.5

Kalikan $- 2$ dengan $18$ .

$- \frac{- 6 {(- x^{2} + 1)}^{\frac{5}{2}} x^{3} + 3 {(- x^{2} + 1)}^{\frac{5}{2}} x + 6 {(1 - x^{2})}^{\frac{3}{2}} x - 12 {(1 - x^{2})}^{\frac{3}{2}} x^{3} + 6 {(1 - x^{2})}^{\frac{3}{2}} x^{5} + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{3} - 36 {(1 - x^{2})}^{\frac{1}{2}} x^{5} + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{2} x^{5}}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.14.6

Kalikan $x^{2}$ dengan $x^{5}$ dengan menambahkan eksponennya.

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Langkah 4.56.6.14.6.1

Pindahkan $x^{5}$ .

$- \frac{- 6 {(- x^{2} + 1)}^{\frac{5}{2}} x^{3} + 3 {(- x^{2} + 1)}^{\frac{5}{2}} x + 6 {(1 - x^{2})}^{\frac{3}{2}} x - 12 {(1 - x^{2})}^{\frac{3}{2}} x^{3} + 6 {(1 - x^{2})}^{\frac{3}{2}} x^{5} + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{3} - 36 {(1 - x^{2})}^{\frac{1}{2}} x^{5} + 18 {(1 - x^{2})}^{\frac{1}{2}} (x^{5} x^{2})}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.14.6.2

Gunakan kaidah pangkat $a^{m} a^{n} = a^{m + n}$ untuk menggabungkan pangkat.

$- \frac{- 6 {(- x^{2} + 1)}^{\frac{5}{2}} x^{3} + 3 {(- x^{2} + 1)}^{\frac{5}{2}} x + 6 {(1 - x^{2})}^{\frac{3}{2}} x - 12 {(1 - x^{2})}^{\frac{3}{2}} x^{3} + 6 {(1 - x^{2})}^{\frac{3}{2}} x^{5} + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{3} - 36 {(1 - x^{2})}^{\frac{1}{2}} x^{5} + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{5 + 2}}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.14.6.3

Tambahkan $5$ dan $2$ .

$- \frac{- 6 {(- x^{2} + 1)}^{\frac{5}{2}} x^{3} + 3 {(- x^{2} + 1)}^{\frac{5}{2}} x + 6 {(1 - x^{2})}^{\frac{3}{2}} x - 12 {(1 - x^{2})}^{\frac{3}{2}} x^{3} + 6 {(1 - x^{2})}^{\frac{3}{2}} x^{5} + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{3} - 36 {(1 - x^{2})}^{\frac{1}{2}} x^{5} + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{7}}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.15

Tulis kembali $- 6 {(- x^{2} + 1)}^{\frac{5}{2}} x^{3} + 3 {(- x^{2} + 1)}^{\frac{5}{2}} x + 6 {(1 - x^{2})}^{\frac{3}{2}} x - 12 {(1 - x^{2})}^{\frac{3}{2}} x^{3} + 6 {(1 - x^{2})}^{\frac{3}{2}} x^{5} + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{3} - 36 {(1 - x^{2})}^{\frac{1}{2}} x^{5} + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{7}$ dalam bentuk faktor.

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Langkah 4.56.6.15.1

Faktorkan $3 x$ dari $- 6 {(- x^{2} + 1)}^{\frac{5}{2}} x^{3} + 3 {(- x^{2} + 1)}^{\frac{5}{2}} x + 6 {(1 - x^{2})}^{\frac{3}{2}} x - 12 {(1 - x^{2})}^{\frac{3}{2}} x^{3} + 6 {(1 - x^{2})}^{\frac{3}{2}} x^{5} + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{3} - 36 {(1 - x^{2})}^{\frac{1}{2}} x^{5} + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{7}$ .

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Langkah 4.56.6.15.1.1

Faktorkan $3 x$ dari $- 6 {(- x^{2} + 1)}^{\frac{5}{2}} x^{3}$ .

$- \frac{3 x (- 2 {(- x^{2} + 1)}^{\frac{5}{2}} x^{2}) + 3 {(- x^{2} + 1)}^{\frac{5}{2}} x + 6 {(1 - x^{2})}^{\frac{3}{2}} x - 12 {(1 - x^{2})}^{\frac{3}{2}} x^{3} + 6 {(1 - x^{2})}^{\frac{3}{2}} x^{5} + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{3} - 36 {(1 - x^{2})}^{\frac{1}{2}} x^{5} + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{7}}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.15.1.2

Faktorkan $3 x$ dari $3 {(- x^{2} + 1)}^{\frac{5}{2}} x$ .

$- \frac{3 x (- 2 {(- x^{2} + 1)}^{\frac{5}{2}} x^{2}) + 3 x ({(- x^{2} + 1)}^{\frac{5}{2}}) + 6 {(1 - x^{2})}^{\frac{3}{2}} x - 12 {(1 - x^{2})}^{\frac{3}{2}} x^{3} + 6 {(1 - x^{2})}^{\frac{3}{2}} x^{5} + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{3} - 36 {(1 - x^{2})}^{\frac{1}{2}} x^{5} + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{7}}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.15.1.3

Faktorkan $3 x$ dari $6 {(1 - x^{2})}^{\frac{3}{2}} x$ .

$- \frac{3 x (- 2 {(- x^{2} + 1)}^{\frac{5}{2}} x^{2}) + 3 x ({(- x^{2} + 1)}^{\frac{5}{2}}) + 3 x (2 {(1 - x^{2})}^{\frac{3}{2}}) - 12 {(1 - x^{2})}^{\frac{3}{2}} x^{3} + 6 {(1 - x^{2})}^{\frac{3}{2}} x^{5} + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{3} - 36 {(1 - x^{2})}^{\frac{1}{2}} x^{5} + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{7}}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.15.1.4

Faktorkan $3 x$ dari $- 12 {(1 - x^{2})}^{\frac{3}{2}} x^{3}$ .

$- \frac{3 x (- 2 {(- x^{2} + 1)}^{\frac{5}{2}} x^{2}) + 3 x ({(- x^{2} + 1)}^{\frac{5}{2}}) + 3 x (2 {(1 - x^{2})}^{\frac{3}{2}}) + 3 x (- 4 {(1 - x^{2})}^{\frac{3}{2}} x^{2}) + 6 {(1 - x^{2})}^{\frac{3}{2}} x^{5} + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{3} - 36 {(1 - x^{2})}^{\frac{1}{2}} x^{5} + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{7}}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.15.1.5

Faktorkan $3 x$ dari $6 {(1 - x^{2})}^{\frac{3}{2}} x^{5}$ .

$- \frac{3 x (- 2 {(- x^{2} + 1)}^{\frac{5}{2}} x^{2}) + 3 x ({(- x^{2} + 1)}^{\frac{5}{2}}) + 3 x (2 {(1 - x^{2})}^{\frac{3}{2}}) + 3 x (- 4 {(1 - x^{2})}^{\frac{3}{2}} x^{2}) + 3 x (2 {(1 - x^{2})}^{\frac{3}{2}} x^{4}) + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{3} - 36 {(1 - x^{2})}^{\frac{1}{2}} x^{5} + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{7}}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.15.1.6

Faktorkan $3 x$ dari $18 {(1 - x^{2})}^{\frac{1}{2}} x^{3}$ .

$- \frac{3 x (- 2 {(- x^{2} + 1)}^{\frac{5}{2}} x^{2}) + 3 x ({(- x^{2} + 1)}^{\frac{5}{2}}) + 3 x (2 {(1 - x^{2})}^{\frac{3}{2}}) + 3 x (- 4 {(1 - x^{2})}^{\frac{3}{2}} x^{2}) + 3 x (2 {(1 - x^{2})}^{\frac{3}{2}} x^{4}) + 3 x (6 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) - 36 {(1 - x^{2})}^{\frac{1}{2}} x^{5} + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{7}}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.15.1.7

Faktorkan $3 x$ dari $- 36 {(1 - x^{2})}^{\frac{1}{2}} x^{5}$ .

$- \frac{3 x (- 2 {(- x^{2} + 1)}^{\frac{5}{2}} x^{2}) + 3 x ({(- x^{2} + 1)}^{\frac{5}{2}}) + 3 x (2 {(1 - x^{2})}^{\frac{3}{2}}) + 3 x (- 4 {(1 - x^{2})}^{\frac{3}{2}} x^{2}) + 3 x (2 {(1 - x^{2})}^{\frac{3}{2}} x^{4}) + 3 x (6 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) + 3 x (- 12 {(1 - x^{2})}^{\frac{1}{2}} x^{4}) + 18 {(1 - x^{2})}^{\frac{1}{2}} x^{7}}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.15.1.8

Faktorkan $3 x$ dari $18 {(1 - x^{2})}^{\frac{1}{2}} x^{7}$ .

$- \frac{3 x (- 2 {(- x^{2} + 1)}^{\frac{5}{2}} x^{2}) + 3 x ({(- x^{2} + 1)}^{\frac{5}{2}}) + 3 x (2 {(1 - x^{2})}^{\frac{3}{2}}) + 3 x (- 4 {(1 - x^{2})}^{\frac{3}{2}} x^{2}) + 3 x (2 {(1 - x^{2})}^{\frac{3}{2}} x^{4}) + 3 x (6 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) + 3 x (- 12 {(1 - x^{2})}^{\frac{1}{2}} x^{4}) + 3 x (6 {(1 - x^{2})}^{\frac{1}{2}} x^{6})}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.15.1.9

Faktorkan $3 x$ dari $3 x (- 2 {(- x^{2} + 1)}^{\frac{5}{2}} x^{2}) + 3 x ({(- x^{2} + 1)}^{\frac{5}{2}})$ .

$- \frac{3 x (- 2 {(- x^{2} + 1)}^{\frac{5}{2}} x^{2} + {(- x^{2} + 1)}^{\frac{5}{2}}) + 3 x (2 {(1 - x^{2})}^{\frac{3}{2}}) + 3 x (- 4 {(1 - x^{2})}^{\frac{3}{2}} x^{2}) + 3 x (2 {(1 - x^{2})}^{\frac{3}{2}} x^{4}) + 3 x (6 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) + 3 x (- 12 {(1 - x^{2})}^{\frac{1}{2}} x^{4}) + 3 x (6 {(1 - x^{2})}^{\frac{1}{2}} x^{6})}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.15.1.10

Faktorkan $3 x$ dari $3 x (- 2 {(- x^{2} + 1)}^{\frac{5}{2}} x^{2} + {(- x^{2} + 1)}^{\frac{5}{2}}) + 3 x (2 {(1 - x^{2})}^{\frac{3}{2}})$ .

$- \frac{3 x (- 2 {(- x^{2} + 1)}^{\frac{5}{2}} x^{2} + {(- x^{2} + 1)}^{\frac{5}{2}} + 2 {(1 - x^{2})}^{\frac{3}{2}}) + 3 x (- 4 {(1 - x^{2})}^{\frac{3}{2}} x^{2}) + 3 x (2 {(1 - x^{2})}^{\frac{3}{2}} x^{4}) + 3 x (6 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) + 3 x (- 12 {(1 - x^{2})}^{\frac{1}{2}} x^{4}) + 3 x (6 {(1 - x^{2})}^{\frac{1}{2}} x^{6})}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.15.1.11

Faktorkan $3 x$ dari $3 x (- 2 {(- x^{2} + 1)}^{\frac{5}{2}} x^{2} + {(- x^{2} + 1)}^{\frac{5}{2}} + 2 {(1 - x^{2})}^{\frac{3}{2}}) + 3 x (- 4 {(1 - x^{2})}^{\frac{3}{2}} x^{2})$ .

$- \frac{3 x (- 2 {(- x^{2} + 1)}^{\frac{5}{2}} x^{2} + {(- x^{2} + 1)}^{\frac{5}{2}} + 2 {(1 - x^{2})}^{\frac{3}{2}} - 4 {(1 - x^{2})}^{\frac{3}{2}} x^{2}) + 3 x (2 {(1 - x^{2})}^{\frac{3}{2}} x^{4}) + 3 x (6 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) + 3 x (- 12 {(1 - x^{2})}^{\frac{1}{2}} x^{4}) + 3 x (6 {(1 - x^{2})}^{\frac{1}{2}} x^{6})}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.15.1.12

Faktorkan $3 x$ dari $3 x (- 2 {(- x^{2} + 1)}^{\frac{5}{2}} x^{2} + {(- x^{2} + 1)}^{\frac{5}{2}} + 2 {(1 - x^{2})}^{\frac{3}{2}} - 4 {(1 - x^{2})}^{\frac{3}{2}} x^{2}) + 3 x (2 {(1 - x^{2})}^{\frac{3}{2}} x^{4})$ .

$- \frac{3 x (- 2 {(- x^{2} + 1)}^{\frac{5}{2}} x^{2} + {(- x^{2} + 1)}^{\frac{5}{2}} + 2 {(1 - x^{2})}^{\frac{3}{2}} - 4 {(1 - x^{2})}^{\frac{3}{2}} x^{2} + 2 {(1 - x^{2})}^{\frac{3}{2}} x^{4}) + 3 x (6 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) + 3 x (- 12 {(1 - x^{2})}^{\frac{1}{2}} x^{4}) + 3 x (6 {(1 - x^{2})}^{\frac{1}{2}} x^{6})}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.15.1.13

Faktorkan $3 x$ dari $3 x (- 2 {(- x^{2} + 1)}^{\frac{5}{2}} x^{2} + {(- x^{2} + 1)}^{\frac{5}{2}} + 2 {(1 - x^{2})}^{\frac{3}{2}} - 4 {(1 - x^{2})}^{\frac{3}{2}} x^{2} + 2 {(1 - x^{2})}^{\frac{3}{2}} x^{4}) + 3 x (6 {(1 - x^{2})}^{\frac{1}{2}} x^{2})$ .

$- \frac{3 x (- 2 {(- x^{2} + 1)}^{\frac{5}{2}} x^{2} + {(- x^{2} + 1)}^{\frac{5}{2}} + 2 {(1 - x^{2})}^{\frac{3}{2}} - 4 {(1 - x^{2})}^{\frac{3}{2}} x^{2} + 2 {(1 - x^{2})}^{\frac{3}{2}} x^{4} + 6 {(1 - x^{2})}^{\frac{1}{2}} x^{2}) + 3 x (- 12 {(1 - x^{2})}^{\frac{1}{2}} x^{4}) + 3 x (6 {(1 - x^{2})}^{\frac{1}{2}} x^{6})}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.15.1.14

$- \frac{3 x (- 2 {(- x^{2} + 1)}^{\frac{5}{2}} x^{2} + {(- x^{2} + 1)}^{\frac{5}{2}} + 2 {(1 - x^{2})}^{\frac{3}{2}} - 4 {(1 - x^{2})}^{\frac{3}{2}} x^{2} + 2 {(1 - x^{2})}^{\frac{3}{2}} x^{4} + 6 {(1 - x^{2})}^{\frac{1}{2}} x^{2} - 12 {(1 - x^{2})}^{\frac{1}{2}} x^{4}) + 3 x (6 {(1 - x^{2})}^{\frac{1}{2}} x^{6})}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.15.1.15

$- \frac{3 x (- 2 {(- x^{2} + 1)}^{\frac{5}{2}} x^{2} + {(- x^{2} + 1)}^{\frac{5}{2}} + 2 {(1 - x^{2})}^{\frac{3}{2}} - 4 {(1 - x^{2})}^{\frac{3}{2}} x^{2} + 2 {(1 - x^{2})}^{\frac{3}{2}} x^{4} + 6 {(1 - x^{2})}^{\frac{1}{2}} x^{2} - 12 {(1 - x^{2})}^{\frac{1}{2}} x^{4} + 6 {(1 - x^{2})}^{\frac{1}{2}} x^{6})}{{(1 - x^{2})}^{6}}$

Langkah 4.56.6.15.2

Susun kembali suku-suku.

$f^{4} (x) = - \frac{3 x (- 2 x^{2} {(- x^{2} + 1)}^{\frac{5}{2}} - 4 x^{2} {(1 - x^{2})}^{\frac{3}{2}} + 2 x^{4} {(1 - x^{2})}^{\frac{3}{2}} + 6 x^{2} {(1 - x^{2})}^{\frac{1}{2}} - 12 x^{4} {(1 - x^{2})}^{\frac{1}{2}} + 6 x^{6} {(1 - x^{2})}^{\frac{1}{2}} + 2 {(1 - x^{2})}^{\frac{3}{2}} + {(- x^{2} + 1)}^{\frac{5}{2}})}{{(1 - x^{2})}^{6}}$