Cálculo Exemplos

$f (x) = \sin (\sqrt{\cos (\sqrt{1 - x^{2}})})$

Etapa 1

Aplique regras básicas de expoentes.

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Etapa 1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ para reescrever $\sqrt{1 - x^{2}}$ como ${(1 - x^{2})}^{\frac{1}{2}}$ .

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

Etapa 1.2

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ para reescrever $\sqrt{\cos ({(1 - x^{2})}^{\frac{1}{2}})}$ como ${\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}$ .

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

Etapa 2

Diferencie usando a regra da cadeia, que determina que $\frac{d}{d x} [f (g (x))]$ é $f' (g (x)) g' (x)$ , em que $f (x) = \sin (x)$ e $g (x) = {\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}$ .

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Etapa 2.1

Para aplicar a regra da cadeia, defina $u_{1}$ como ${\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}$ .

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

Etapa 2.2

A derivada de $\sin (u_{1})$ em relação a $u_{1}$ é $\cos (u_{1})$ .

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

Etapa 2.3

Substitua todas as ocorrências de $u_{1}$ por ${\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}$ .

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

Etapa 3

Diferencie usando a regra da cadeia, que determina que $\frac{d}{d x} [f (g (x))]$ é $f' (g (x)) g' (x)$ , em que $f (x) = x^{\frac{1}{2}}$ e $g (x) = \cos ({(1 - x^{2})}^{\frac{1}{2}})$ .

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Etapa 3.1

Para aplicar a regra da cadeia, defina $u_{2}$ como $\cos ({(1 - x^{2})}^{\frac{1}{2}})$ .

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

Etapa 3.2

Diferencie usando a regra da multiplicação de potências, que determina que $\frac{d}{d u_{2}} [{u_{2}}^{n}]$ é $n {u_{2}}^{n - 1}$ , em que $n = \frac{1}{2}$ .

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

Etapa 3.3

Substitua todas as ocorrências de $u_{2}$ por $\cos ({(1 - x^{2})}^{\frac{1}{2}})$ .

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

Etapa 4

Para escrever $- 1$ como fração com um denominador comum, multiplique por $\frac{2}{2}$ .

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

Etapa 5

Combine $- 1$ e $\frac{2}{2}$ .

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

Etapa 6

Combine os numeradores em relação ao denominador comum.

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

Etapa 7

Simplifique o numerador.

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Etapa 7.1

Multiplique $- 1$ por $2$ .

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

Etapa 7.2

Subtraia $2$ de $1$ .

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

Etapa 8

Combine frações.

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Etapa 8.1

Mova o número negativo para a frente da fração.

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

Etapa 8.2

Combine $\frac{1}{2}$ e ${\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{- \frac{1}{2}}$ .

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

Etapa 8.3

Mova ${\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{- \frac{1}{2}}$ para o denominador usando a regra do expoente negativo $b^{- n} = \frac{1}{b^{n}}$ .

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

Etapa 8.4

Combine $\frac{1}{2 {\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}}$ e $\cos ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}})$ .

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

Etapa 9

Diferencie usando a regra da cadeia, que determina que $\frac{d}{d x} [f (g (x))]$ é $f' (g (x)) g' (x)$ , em que $f (x) = \cos (x)$ e $g (x) = {(1 - x^{2})}^{\frac{1}{2}}$ .

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Etapa 9.1

Para aplicar a regra da cadeia, defina $u_{3}$ como ${(1 - x^{2})}^{\frac{1}{2}}$ .

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

Etapa 9.2

A derivada de $\cos (u_{3})$ em relação a $u_{3}$ é $- \sin (u_{3})$ .

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

Etapa 9.3

Substitua todas as ocorrências de $u_{3}$ por ${(1 - x^{2})}^{\frac{1}{2}}$ .

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

Etapa 10

Combine $\frac{\cos ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}})}{2 {\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}}$ e $\sin ({(1 - x^{2})}^{\frac{1}{2}})$ .

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

Etapa 11

Diferencie usando a regra da cadeia, que determina que $\frac{d}{d x} [f (g (x))]$ é $f' (g (x)) g' (x)$ , em que $f (x) = x^{\frac{1}{2}}$ e $g (x) = 1 - x^{2}$ .

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Etapa 11.1

Para aplicar a regra da cadeia, defina $u_{4}$ como $1 - x^{2}$ .

$- \frac{\cos ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}) \sin ({(1 - x^{2})}^{\frac{1}{2}})}{2 {\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}} (\frac{d}{d u_{4}} [{u_{4}}^{\frac{1}{2}}] \frac{d}{d x} [1 - x^{2}])$

Etapa 11.2

Diferencie usando a regra da multiplicação de potências, que determina que $\frac{d}{d u_{4}} [{u_{4}}^{n}]$ é $n {u_{4}}^{n - 1}$ , em que $n = \frac{1}{2}$ .

$- \frac{\cos ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}) \sin ({(1 - x^{2})}^{\frac{1}{2}})}{2 {\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}} (\frac{1}{2} {u_{4}}^{\frac{1}{2} - 1} \frac{d}{d x} [1 - x^{2}])$

Etapa 11.3

Substitua todas as ocorrências de $u_{4}$ por $1 - x^{2}$ .

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

Etapa 12

Para escrever $- 1$ como fração com um denominador comum, multiplique por $\frac{2}{2}$ .

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

Etapa 13

Combine $- 1$ e $\frac{2}{2}$ .

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

Etapa 14

Combine os numeradores em relação ao denominador comum.

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

Etapa 15

Simplifique o numerador.

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Etapa 15.1

Multiplique $- 1$ por $2$ .

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

Etapa 15.2

Subtraia $2$ de $1$ .

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

Etapa 16

Combine frações.

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Etapa 16.1

Mova o número negativo para a frente da fração.

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

Etapa 16.2

Combine $\frac{1}{2}$ e ${(1 - x^{2})}^{- \frac{1}{2}}$ .

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

Etapa 16.3

Mova ${(1 - x^{2})}^{- \frac{1}{2}}$ para o denominador usando a regra do expoente negativo $b^{- n} = \frac{1}{b^{n}}$ .

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

Etapa 16.4

Multiplique $\frac{1}{2 {(1 - x^{2})}^{\frac{1}{2}}}$ por $\frac{\cos ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}) \sin ({(1 - x^{2})}^{\frac{1}{2}})}{2 {\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}}$ .

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

Etapa 16.5

Multiplique $2$ por $2$ .

$- \frac{\cos ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}) \sin ({(1 - x^{2})}^{\frac{1}{2}})}{4 {(1 - x^{2})}^{\frac{1}{2}} {\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}} \frac{d}{d x} [1 - x^{2}]$

Etapa 17

De acordo com a regra da soma, a derivada de $1 - x^{2}$ com relação a $x$ é $\frac{d}{d x} [1] + \frac{d}{d x} [- x^{2}]$ .

Etapa 18

Como $1$ é constante em relação a $x$ , a derivada de $1$ em relação a $x$ é $0$ .

Etapa 19

Some $0$ e $\frac{d}{d x} [- x^{2}]$ .

Etapa 20

Como $- 1$ é constante em relação a $x$ , a derivada de $- x^{2}$ em relação a $x$ é $- \frac{d}{d x} [x^{2}]$ .

Etapa 21

Multiplique.

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Etapa 21.1

Multiplique $- 1$ por $- 1$ .

$1 \frac{\cos ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}) \sin ({(1 - x^{2})}^{\frac{1}{2}})}{4 {(1 - x^{2})}^{\frac{1}{2}} {\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}} \frac{d}{d x} [x^{2}]$

Etapa 21.2

Multiplique $\frac{\cos ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}) \sin ({(1 - x^{2})}^{\frac{1}{2}})}{4 {(1 - x^{2})}^{\frac{1}{2}} {\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}}$ por $1$ .

$\frac{\cos ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}) \sin ({(1 - x^{2})}^{\frac{1}{2}})}{4 {(1 - x^{2})}^{\frac{1}{2}} {\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}} \frac{d}{d x} [x^{2}]$

Etapa 22

Diferencie usando a regra da multiplicação de potências, que determina que $\frac{d}{d x} [x^{n}]$ é $n x^{n - 1}$ , em que $n = 2$ .

$\frac{\cos ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}) \sin ({(1 - x^{2})}^{\frac{1}{2}})}{4 {(1 - x^{2})}^{\frac{1}{2}} {\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}} (2 x)$

Etapa 23

Simplifique os termos.

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Etapa 23.1

Combine $2$ e $\frac{\cos ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}) \sin ({(1 - x^{2})}^{\frac{1}{2}})}{4 {(1 - x^{2})}^{\frac{1}{2}} {\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}}$ .

$\frac{2 (\cos ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}) \sin ({(1 - x^{2})}^{\frac{1}{2}}))}{4 {(1 - x^{2})}^{\frac{1}{2}} {\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}} x$

Etapa 23.2

Combine $\frac{2 (\cos ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}) \sin ({(1 - x^{2})}^{\frac{1}{2}}))}{4 {(1 - x^{2})}^{\frac{1}{2}} {\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}}$ e $x$ .

$\frac{2 (\cos ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}) \sin ({(1 - x^{2})}^{\frac{1}{2}})) x}{4 {(1 - x^{2})}^{\frac{1}{2}} {\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}}$

Etapa 23.3

Fatore $2$ de $2 \cos ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}) \sin ({(1 - x^{2})}^{\frac{1}{2}}) x$ .

$\frac{2 (\cos ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}) \sin ({(1 - x^{2})}^{\frac{1}{2}}) x)}{4 {(1 - x^{2})}^{\frac{1}{2}} {\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}}$

Etapa 24

Cancele os fatores comuns.

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Etapa 24.1

Fatore $2$ de $4 {(1 - x^{2})}^{\frac{1}{2}} {\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}$ .

$\frac{2 (\cos ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}) \sin ({(1 - x^{2})}^{\frac{1}{2}}) x)}{2 (2 {(1 - x^{2})}^{\frac{1}{2}} {\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}})}$

Etapa 24.2

Cancele o fator comum.

$\frac{2 (\cos ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}) \sin ({(1 - x^{2})}^{\frac{1}{2}}) x)}{2 (2 {(1 - x^{2})}^{\frac{1}{2}} {\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}})}$

Etapa 24.3

Reescreva a expressão.

$\frac{\cos ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}) \sin ({(1 - x^{2})}^{\frac{1}{2}}) x}{2 {(1 - x^{2})}^{\frac{1}{2}} {\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}}$

Etapa 25

Reordene os termos.

$\frac{x \cos ({\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}) \sin ({(1 - x^{2})}^{\frac{1}{2}})}{2 {\cos ({(1 - x^{2})}^{\frac{1}{2}})}^{\frac{1}{2}} {(1 - x^{2})}^{\frac{1}{2}}}$