Cálculo Exemplos

$\frac{(x^{2} - 3 x^{x} + 2 x - 1) d x}{x^{2} - 4 x + 4}$

Etapa 1

Diferencie usando a regra do quociente, que determina que $\frac{d}{d x} [\frac{f (x)}{g (x)}]$ é $\frac{g (x) \frac{d}{d x} [f (x)] - f (x) \frac{d}{d x} [g (x)]}{{g (x)}^{2}}$ , em que $f (x) = (x^{2} - 3 x^{x} + 2 x - 1) d x$ e $g (x) = x^{2} - 4 x + 4$ .

$\frac{(x^{2} - 4 x + 4) \frac{d}{d x} [(x^{2} - 3 x^{x} + 2 x - 1) d x] - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 4 x + 4]}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 2

Como $d$ é constante em relação a $x$ , a derivada de $(x^{2} - 3 x^{x} + 2 x - 1) d x$ em relação a $x$ é $d \frac{d}{d x} [(x^{2} - 3 x^{x} + 2 x - 1) x]$ .

$\frac{(x^{2} - 4 x + 4) (d \frac{d}{d x} [(x^{2} - 3 x^{x} + 2 x - 1) x]) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 4 x + 4]}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 3

Diferencie usando a regra do produto, que determina que $\frac{d}{d x} [f (x) g (x)]$ é $f (x) \frac{d}{d x} [g (x)] + g (x) \frac{d}{d x} [f (x)]$ , em que $f (x) = x^{2} - 3 x^{x} + 2 x - 1$ e $g (x) = x$ .

$\frac{(x^{2} - 4 x + 4) (d ((x^{2} - 3 x^{x} + 2 x - 1) \frac{d}{d x} [x] + x \frac{d}{d x} [x^{2} - 3 x^{x} + 2 x - 1])) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 4 x + 4]}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 4

Diferencie.

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Etapa 4.1

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

$\frac{(x^{2} - 4 x + 4) (d ((x^{2} - 3 x^{x} + 2 x - 1) \cdot 1 + x \frac{d}{d x} [x^{2} - 3 x^{x} + 2 x - 1])) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 4 x + 4]}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 4.2

Multiplique $x^{2} - 3 x^{x} + 2 x - 1$ por $1$ .

$\frac{(x^{2} - 4 x + 4) (d (x^{2} - 3 x^{x} + 2 x - 1 + x \frac{d}{d x} [x^{2} - 3 x^{x} + 2 x - 1])) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 4 x + 4]}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 4.3

De acordo com a regra da soma, a derivada de $x^{2} - 3 x^{x} + 2 x - 1$ com relação a $x$ é $\frac{d}{d x} [x^{2}] + \frac{d}{d x} [- 3 x^{x}] + \frac{d}{d x} [2 x] + \frac{d}{d x} [- 1]$ .

$\frac{(x^{2} - 4 x + 4) (d (x^{2} - 3 x^{x} + 2 x - 1 + x (\frac{d}{d x} [x^{2}] + \frac{d}{d x} [- 3 x^{x}] + \frac{d}{d x} [2 x] + \frac{d}{d x} [- 1]))) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 4 x + 4]}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 4.4

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

$\frac{(x^{2} - 4 x + 4) (d (x^{2} - 3 x^{x} + 2 x - 1 + x (2 x + \frac{d}{d x} [- 3 x^{x}] + \frac{d}{d x} [2 x] + \frac{d}{d x} [- 1]))) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 4 x + 4]}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 4.5

Como $- 3$ é constante em relação a $x$ , a derivada de $- 3 x^{x}$ em relação a $x$ é $- 3 \frac{d}{d x} [x^{x}]$ .

$\frac{(x^{2} - 4 x + 4) (d (x^{2} - 3 x^{x} + 2 x - 1 + x (2 x - 3 \frac{d}{d x} [x^{x}] + \frac{d}{d x} [2 x] + \frac{d}{d x} [- 1]))) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 4 x + 4]}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 5

Use as propriedades dos logaritmos para simplificar a diferenciação.

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Etapa 5.1

Reescreva $x^{x}$ como $e^{\ln (x^{x})}$ .

$\frac{(x^{2} - 4 x + 4) (d (x^{2} - 3 x^{x} + 2 x - 1 + x (2 x - 3 \frac{d}{d x} [e^{\ln (x^{x})}] + \frac{d}{d x} [2 x] + \frac{d}{d x} [- 1]))) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 4 x + 4]}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 5.2

Expanda $\ln (x^{x})$ movendo $x$ para fora do logaritmo.

$\frac{(x^{2} - 4 x + 4) (d (x^{2} - 3 x^{x} + 2 x - 1 + x (2 x - 3 \frac{d}{d x} [e^{x \ln (x)}] + \frac{d}{d x} [2 x] + \frac{d}{d x} [- 1]))) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 4 x + 4]}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 6

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

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Etapa 6.1

Para aplicar a regra da cadeia, defina $u$ como $x \ln (x)$ .

$\frac{(x^{2} - 4 x + 4) (d (x^{2} - 3 x^{x} + 2 x - 1 + x (2 x - 3 (\frac{d}{d u} [e^{u}] \frac{d}{d x} [x \ln (x)]) + \frac{d}{d x} [2 x] + \frac{d}{d x} [- 1]))) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 4 x + 4]}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 6.2

Diferencie usando a regra exponencial, que determina que $\frac{d}{d u} [a^{u}]$ é $a^{u} \ln (a)$ , em que $a$ = $e$ .

$\frac{(x^{2} - 4 x + 4) (d (x^{2} - 3 x^{x} + 2 x - 1 + x (2 x - 3 (e^{u} \frac{d}{d x} [x \ln (x)]) + \frac{d}{d x} [2 x] + \frac{d}{d x} [- 1]))) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 4 x + 4]}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 6.3

Substitua todas as ocorrências de $u$ por $x \ln (x)$ .

$\frac{(x^{2} - 4 x + 4) (d (x^{2} - 3 x^{x} + 2 x - 1 + x (2 x - 3 (e^{x \ln (x)} \frac{d}{d x} [x \ln (x)]) + \frac{d}{d x} [2 x] + \frac{d}{d x} [- 1]))) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 4 x + 4]}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 7

Diferencie usando a regra do produto, que determina que $\frac{d}{d x} [f (x) g (x)]$ é $f (x) \frac{d}{d x} [g (x)] + g (x) \frac{d}{d x} [f (x)]$ , em que $f (x) = x$ e $g (x) = \ln (x)$ .

$\frac{(x^{2} - 4 x + 4) (d (x^{2} - 3 x^{x} + 2 x - 1 + x (2 x - 3 e^{x \ln (x)} (x \frac{d}{d x} [\ln (x)] + \ln (x) \frac{d}{d x} [x]) + \frac{d}{d x} [2 x] + \frac{d}{d x} [- 1]))) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 4 x + 4]}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 8

A derivada de $\ln (x)$ em relação a $x$ é $\frac{1}{x}$ .

$\frac{(x^{2} - 4 x + 4) (d (x^{2} - 3 x^{x} + 2 x - 1 + x (2 x - 3 e^{x \ln (x)} (x \frac{1}{x} + \ln (x) \frac{d}{d x} [x]) + \frac{d}{d x} [2 x] + \frac{d}{d x} [- 1]))) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 4 x + 4]}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 9

Diferencie.

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Etapa 9.1

Combine $x$ e $\frac{1}{x}$ .

$\frac{(x^{2} - 4 x + 4) (d (x^{2} - 3 x^{x} + 2 x - 1 + x (2 x - 3 e^{x \ln (x)} (\frac{x}{x} + \ln (x) \frac{d}{d x} [x]) + \frac{d}{d x} [2 x] + \frac{d}{d x} [- 1]))) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 4 x + 4]}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 9.2

Cancele o fator comum de $x$ .

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Etapa 9.2.1

Cancele o fator comum.

Etapa 9.2.2

Reescreva a expressão.

$\frac{(x^{2} - 4 x + 4) (d (x^{2} - 3 x^{x} + 2 x - 1 + x (2 x - 3 e^{x \ln (x)} (1 + \ln (x) \frac{d}{d x} [x]) + \frac{d}{d x} [2 x] + \frac{d}{d x} [- 1]))) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 4 x + 4]}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 9.3

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

$\frac{(x^{2} - 4 x + 4) (d (x^{2} - 3 x^{x} + 2 x - 1 + x (2 x - 3 e^{x \ln (x)} (1 + \ln (x) \cdot 1) + \frac{d}{d x} [2 x] + \frac{d}{d x} [- 1]))) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 4 x + 4]}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 9.4

Multiplique $\ln (x)$ por $1$ .

$\frac{(x^{2} - 4 x + 4) (d (x^{2} - 3 x^{x} + 2 x - 1 + x (2 x - 3 e^{x \ln (x)} (1 + \ln (x)) + \frac{d}{d x} [2 x] + \frac{d}{d x} [- 1]))) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 4 x + 4]}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 9.5

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

$\frac{(x^{2} - 4 x + 4) (d (x^{2} - 3 x^{x} + 2 x - 1 + x (2 x - 3 e^{x \ln (x)} (1 + \ln (x)) + 2 \frac{d}{d x} [x] + \frac{d}{d x} [- 1]))) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 4 x + 4]}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 9.6

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

$\frac{(x^{2} - 4 x + 4) (d (x^{2} - 3 x^{x} + 2 x - 1 + x (2 x - 3 e^{x \ln (x)} (1 + \ln (x)) + 2 \cdot 1 + \frac{d}{d x} [- 1]))) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 4 x + 4]}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 9.7

Multiplique $2$ por $1$ .

$\frac{(x^{2} - 4 x + 4) (d (x^{2} - 3 x^{x} + 2 x - 1 + x (2 x - 3 e^{x \ln (x)} (1 + \ln (x)) + 2 + \frac{d}{d x} [- 1]))) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 4 x + 4]}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 9.8

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

$\frac{(x^{2} - 4 x + 4) (d (x^{2} - 3 x^{x} + 2 x - 1 + x (2 x - 3 e^{x \ln (x)} (1 + \ln (x)) + 2 + 0))) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 4 x + 4]}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 9.9

Some $2 x - 3 e^{x \ln (x)} (1 + \ln (x)) + 2$ e $0$ .

$\frac{(x^{2} - 4 x + 4) (d (x^{2} - 3 x^{x} + 2 x - 1 + x (2 x - 3 e^{x \ln (x)} (1 + \ln (x)) + 2))) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 4 x + 4]}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 10

Simplifique.

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Etapa 10.1

Aplique a propriedade distributiva.

$\frac{(x^{2} - 4 x + 4) (d (x^{2} - 3 x^{x} + 2 x - 1 + x (2 x - 3 e^{x \ln (x)} \cdot 1 - 3 e^{x \ln (x)} \ln (x) + 2))) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 4 x + 4]}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 10.2

Aplique a propriedade distributiva.

$\frac{(x^{2} - 4 x + 4) (d (x^{2} - 3 x^{x} + 2 x - 1 + x (2 x) + x (- 3 e^{x \ln (x)} \cdot 1) + x (- 3 e^{x \ln (x)} \ln (x)) + x \cdot 2)) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 4 x + 4]}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 10.3

Aplique a propriedade distributiva.

$\frac{(x^{2} - 4 x + 4) (d x^{2} + d (- 3 x^{x}) + d (2 x) + d \cdot - 1 + d (x (2 x)) + d (x (- 3 e^{x \ln (x)} \cdot 1)) + d (x (- 3 e^{x \ln (x)} \ln (x))) + d (x \cdot 2)) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 4 x + 4]}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 10.4

Combine os termos.

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Etapa 10.4.1

Mova $2$ para a esquerda de $d$ .

$\frac{(x^{2} - 4 x + 4) (d x^{2} + d (- 3 x^{x}) + 2 \cdot d x + d \cdot - 1 + d (x (2 x)) + d (x (- 3 e^{x \ln (x)} \cdot 1)) + d (x (- 3 e^{x \ln (x)} \ln (x))) + d (x \cdot 2)) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 4 x + 4]}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 10.4.2

Mova $- 1$ para a esquerda de $d$ .

$\frac{(x^{2} - 4 x + 4) (d x^{2} + d (- 3 x^{x}) + 2 d x - 1 \cdot d + d (x (2 x)) + d (x (- 3 e^{x \ln (x)} \cdot 1)) + d (x (- 3 e^{x \ln (x)} \ln (x))) + d (x \cdot 2)) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 4 x + 4]}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 10.4.3

Reescreva $- 1 d$ como $- d$ .

$\frac{(x^{2} - 4 x + 4) (d x^{2} + d (- 3 x^{x}) + 2 d x - d + d (x (2 x)) + d (x (- 3 e^{x \ln (x)} \cdot 1)) + d (x (- 3 e^{x \ln (x)} \ln (x))) + d (x \cdot 2)) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 4 x + 4]}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 10.4.4

Eleve $x$ à potência de $1$ .

$\frac{(x^{2} - 4 x + 4) (d x^{2} + d (- 3 x^{x}) + 2 d x - d + d (2 (x^{1} x)) + d (x (- 3 e^{x \ln (x)} \cdot 1)) + d (x (- 3 e^{x \ln (x)} \ln (x))) + d (x \cdot 2)) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 4 x + 4]}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 10.4.5

Eleve $x$ à potência de $1$ .

$\frac{(x^{2} - 4 x + 4) (d x^{2} + d (- 3 x^{x}) + 2 d x - d + d (2 (x^{1} x^{1})) + d (x (- 3 e^{x \ln (x)} \cdot 1)) + d (x (- 3 e^{x \ln (x)} \ln (x))) + d (x \cdot 2)) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 4 x + 4]}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 10.4.6

Use a regra da multiplicação de potências $a^{m} a^{n} = a^{m + n}$ para combinar expoentes.

$\frac{(x^{2} - 4 x + 4) (d x^{2} + d (- 3 x^{x}) + 2 d x - d + d (2 x^{1 + 1}) + d (x (- 3 e^{x \ln (x)} \cdot 1)) + d (x (- 3 e^{x \ln (x)} \ln (x))) + d (x \cdot 2)) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 4 x + 4]}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 10.4.7

Some $1$ e $1$ .

$\frac{(x^{2} - 4 x + 4) (d x^{2} + d (- 3 x^{x}) + 2 d x - d + d (2 x^{2}) + d (x (- 3 e^{x \ln (x)} \cdot 1)) + d (x (- 3 e^{x \ln (x)} \ln (x))) + d (x \cdot 2)) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 4 x + 4]}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 10.4.8

Mova $2$ para a esquerda de $d$ .

$\frac{(x^{2} - 4 x + 4) (d x^{2} + d (- 3 x^{x}) + 2 d x - d + 2 \cdot d x^{2} + d (x (- 3 e^{x \ln (x)} \cdot 1)) + d (x (- 3 e^{x \ln (x)} \ln (x))) + d (x \cdot 2)) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 4 x + 4]}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 10.4.9

Multiplique $- 3$ por $1$ .

$\frac{(x^{2} - 4 x + 4) (d x^{2} + d (- 3 x^{x}) + 2 d x - d + 2 d x^{2} + d (x (- 3 e^{x \ln (x)})) + d (x (- 3 e^{x \ln (x)} \ln (x))) + d (x \cdot 2)) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 4 x + 4]}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 10.4.10

Mova $2$ para a esquerda de $x$ .

$\frac{(x^{2} - 4 x + 4) (d x^{2} + d (- 3 x^{x}) + 2 d x - d + 2 d x^{2} + d x (- 3 e^{x \ln (x)}) + d x (- 3 e^{x \ln (x)} \ln (x)) + d (2 \cdot x)) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 4 x + 4]}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 10.4.11

Mova $2$ para a esquerda de $d$ .

$\frac{(x^{2} - 4 x + 4) (d x^{2} + d (- 3 x^{x}) + 2 d x - d + 2 d x^{2} + d x (- 3 e^{x \ln (x)}) + d x (- 3 e^{x \ln (x)} \ln (x)) + 2 \cdot d x) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 4 x + 4]}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 10.4.12

Some $d x^{2}$ e $2 d x^{2}$ .

$\frac{(x^{2} - 4 x + 4) (d (- 3 x^{x}) + 2 d x - d + 3 d x^{2} + d x (- 3 e^{x \ln (x)}) + d x (- 3 e^{x \ln (x)} \ln (x)) + 2 d x) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 4 x + 4]}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 10.4.13

Some $2 d x$ e $2 d x$ .

$\frac{(x^{2} - 4 x + 4) (d (- 3 x^{x}) - d + 3 d x^{2} + d x (- 3 e^{x \ln (x)}) + d x (- 3 e^{x \ln (x)} \ln (x)) + 4 d x) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 4 x + 4]}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 10.5

Reordene os termos.

$\frac{(x^{2} - 4 x + 4) (- d - 3 x^{x} d + 3 x^{2} d - 3 e^{x \ln (x)} d x - 3 e^{x \ln (x)} d x \ln (x) + 4 d x) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 4 x + 4]}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 11

Diferencie.

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Etapa 11.1

De acordo com a regra da soma, a derivada de $x^{2} - 4 x + 4$ com relação a $x$ é $\frac{d}{d x} [x^{2}] + \frac{d}{d x} [- 4 x] + \frac{d}{d x} [4]$ .

$\frac{(x^{2} - 4 x + 4) (- d - 3 x^{x} d + 3 x^{2} d - 3 e^{x \ln (x)} d x - 3 e^{x \ln (x)} d x \ln (x) + 4 d x) - (x^{2} - 3 x^{x} + 2 x - 1) d x (\frac{d}{d x} [x^{2}] + \frac{d}{d x} [- 4 x] + \frac{d}{d x} [4])}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 11.2

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

$\frac{(x^{2} - 4 x + 4) (- d - 3 x^{x} d + 3 x^{2} d - 3 e^{x \ln (x)} d x - 3 e^{x \ln (x)} d x \ln (x) + 4 d x) - (x^{2} - 3 x^{x} + 2 x - 1) d x (2 x + \frac{d}{d x} [- 4 x] + \frac{d}{d x} [4])}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 12

Avalie $\frac{d}{d x} [- 4 x]$ .

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Etapa 12.1

Como $- 4$ é constante em relação a $x$ , a derivada de $- 4 x$ em relação a $x$ é $- 4 \frac{d}{d x} [x]$ .

$\frac{(x^{2} - 4 x + 4) (- d - 3 x^{x} d + 3 x^{2} d - 3 e^{x \ln (x)} d x - 3 e^{x \ln (x)} d x \ln (x) + 4 d x) - (x^{2} - 3 x^{x} + 2 x - 1) d x (2 x - 4 \frac{d}{d x} [x] + \frac{d}{d x} [4])}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 12.2

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

$\frac{(x^{2} - 4 x + 4) (- d - 3 x^{x} d + 3 x^{2} d - 3 e^{x \ln (x)} d x - 3 e^{x \ln (x)} d x \ln (x) + 4 d x) - (x^{2} - 3 x^{x} + 2 x - 1) d x (2 x - 4 \cdot 1 + \frac{d}{d x} [4])}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 12.3

Multiplique $- 4$ por $1$ .

$\frac{(x^{2} - 4 x + 4) (- d - 3 x^{x} d + 3 x^{2} d - 3 e^{x \ln (x)} d x - 3 e^{x \ln (x)} d x \ln (x) + 4 d x) - (x^{2} - 3 x^{x} + 2 x - 1) d x (2 x - 4 + \frac{d}{d x} [4])}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 13

Diferencie usando a regra da constante.

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Etapa 13.1

Como $4$ é constante em relação a $x$ , a derivada de $4$ em relação a $x$ é $0$ .

$\frac{(x^{2} - 4 x + 4) (- d - 3 x^{x} d + 3 x^{2} d - 3 e^{x \ln (x)} d x - 3 e^{x \ln (x)} d x \ln (x) + 4 d x) - (x^{2} - 3 x^{x} + 2 x - 1) d x (2 x - 4 + 0)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 13.2

Some $2 x - 4$ e $0$ .

$\frac{(x^{2} - 4 x + 4) (- d - 3 x^{x} d + 3 x^{2} d - 3 e^{x \ln (x)} d x - 3 e^{x \ln (x)} d x \ln (x) + 4 d x) - (x^{2} - 3 x^{x} + 2 x - 1) d x (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14

Simplifique.

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Etapa 14.1

Aplique a propriedade distributiva.

$\frac{(x^{2} - 4 x + 4) (- d - 3 x^{x} d + 3 x^{2} d - 3 e^{x \ln (x)} d x - 3 e^{x \ln (x)} d x \ln (x) + 4 d x) + (- x^{2} - (- 3 x^{x}) - (2 x) - - 1) d x (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.2

Aplique a propriedade distributiva.

$\frac{(x^{2} - 4 x + 4) (- d - 3 x^{x} d + 3 x^{2} d - 3 e^{x \ln (x)} d x - 3 e^{x \ln (x)} d x \ln (x) + 4 d x) + (- x^{2} d - (- 3 x^{x}) d - (2 x) d - - 1 d) x (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.3

Aplique a propriedade distributiva.

$\frac{(x^{2} - 4 x + 4) (- d - 3 x^{x} d + 3 x^{2} d - 3 e^{x \ln (x)} d x - 3 e^{x \ln (x)} d x \ln (x) + 4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4

Simplifique o numerador.

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Etapa 14.4.1

Simplifique cada termo.

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Etapa 14.4.1.1

Simplifique cada termo.

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Etapa 14.4.1.1.1

Simplifique $- 3 \ln (x)$ movendo $3$ para dentro do logaritmo.

$\frac{(x^{2} - 4 x + 4) (- d - 3 x^{x} d + 3 x^{2} d - 3 e^{x \ln (x)} d x + e^{x \ln (x)} d x (- \ln (x^{3})) + 4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.1.2

Reescreva usando a propriedade comutativa da multiplicação.

$\frac{(x^{2} - 4 x + 4) (- d - 3 x^{x} d + 3 x^{2} d - 3 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{3}) + 4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.2

Expanda $(x^{2} - 4 x + 4) (- d - 3 x^{x} d + 3 x^{2} d - 3 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{3}) + 4 d x)$ multiplicando cada termo na primeira expressão por cada um dos termos na segunda expressão.

$\frac{x^{2} (- d) + x^{2} (- 3 x^{x} d) + x^{2} (3 x^{2} d) + x^{2} (- 3 e^{x \ln (x)} d x) + x^{2} (- e^{x \ln (x)} d x \ln (x^{3})) + x^{2} (4 d x) - 4 x (- d) - 4 x (- 3 x^{x} d) - 4 x (3 x^{2} d) - 4 x (- 3 e^{x \ln (x)} d x) - 4 x (- e^{x \ln (x)} d x \ln (x^{3})) - 4 x (4 d x) + 4 (- d) + 4 (- 3 x^{x} d) + 4 (3 x^{2} d) + 4 (- 3 e^{x \ln (x)} d x) + 4 (- e^{x \ln (x)} d x \ln (x^{3})) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.3

Simplifique cada termo.

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Etapa 14.4.1.3.1

Reescreva usando a propriedade comutativa da multiplicação.

$\frac{- x^{2} d + x^{2} (- 3 x^{x} d) + x^{2} (3 x^{2} d) + x^{2} (- 3 e^{x \ln (x)} d x) + x^{2} (- e^{x \ln (x)} d x \ln (x^{3})) + x^{2} (4 d x) - 4 x (- d) - 4 x (- 3 x^{x} d) - 4 x (3 x^{2} d) - 4 x (- 3 e^{x \ln (x)} d x) - 4 x (- e^{x \ln (x)} d x \ln (x^{3})) - 4 x (4 d x) + 4 (- d) + 4 (- 3 x^{x} d) + 4 (3 x^{2} d) + 4 (- 3 e^{x \ln (x)} d x) + 4 (- e^{x \ln (x)} d x \ln (x^{3})) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.3.2

Reescreva usando a propriedade comutativa da multiplicação.

$\frac{- x^{2} d - 3 x^{2} (x^{x} d) + x^{2} (3 x^{2} d) + x^{2} (- 3 e^{x \ln (x)} d x) + x^{2} (- e^{x \ln (x)} d x \ln (x^{3})) + x^{2} (4 d x) - 4 x (- d) - 4 x (- 3 x^{x} d) - 4 x (3 x^{2} d) - 4 x (- 3 e^{x \ln (x)} d x) - 4 x (- e^{x \ln (x)} d x \ln (x^{3})) - 4 x (4 d x) + 4 (- d) + 4 (- 3 x^{x} d) + 4 (3 x^{2} d) + 4 (- 3 e^{x \ln (x)} d x) + 4 (- e^{x \ln (x)} d x \ln (x^{3})) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.3.3

Multiplique $x^{2}$ por $x^{x}$ somando os expoentes.

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Etapa 14.4.1.3.3.1

Mova $x^{x}$ .

$\frac{- x^{2} d - 3 (x^{x} x^{2}) d + x^{2} (3 x^{2} d) + x^{2} (- 3 e^{x \ln (x)} d x) + x^{2} (- e^{x \ln (x)} d x \ln (x^{3})) + x^{2} (4 d x) - 4 x (- d) - 4 x (- 3 x^{x} d) - 4 x (3 x^{2} d) - 4 x (- 3 e^{x \ln (x)} d x) - 4 x (- e^{x \ln (x)} d x \ln (x^{3})) - 4 x (4 d x) + 4 (- d) + 4 (- 3 x^{x} d) + 4 (3 x^{2} d) + 4 (- 3 e^{x \ln (x)} d x) + 4 (- e^{x \ln (x)} d x \ln (x^{3})) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.3.3.2

Use a regra da multiplicação de potências $a^{m} a^{n} = a^{m + n}$ para combinar expoentes.

$\frac{- x^{2} d - 3 x^{x + 2} d + x^{2} (3 x^{2} d) + x^{2} (- 3 e^{x \ln (x)} d x) + x^{2} (- e^{x \ln (x)} d x \ln (x^{3})) + x^{2} (4 d x) - 4 x (- d) - 4 x (- 3 x^{x} d) - 4 x (3 x^{2} d) - 4 x (- 3 e^{x \ln (x)} d x) - 4 x (- e^{x \ln (x)} d x \ln (x^{3})) - 4 x (4 d x) + 4 (- d) + 4 (- 3 x^{x} d) + 4 (3 x^{2} d) + 4 (- 3 e^{x \ln (x)} d x) + 4 (- e^{x \ln (x)} d x \ln (x^{3})) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.3.4

Reescreva usando a propriedade comutativa da multiplicação.

$\frac{- x^{2} d - 3 x^{x + 2} d + 3 x^{2} (x^{2} d) + x^{2} (- 3 e^{x \ln (x)} d x) + x^{2} (- e^{x \ln (x)} d x \ln (x^{3})) + x^{2} (4 d x) - 4 x (- d) - 4 x (- 3 x^{x} d) - 4 x (3 x^{2} d) - 4 x (- 3 e^{x \ln (x)} d x) - 4 x (- e^{x \ln (x)} d x \ln (x^{3})) - 4 x (4 d x) + 4 (- d) + 4 (- 3 x^{x} d) + 4 (3 x^{2} d) + 4 (- 3 e^{x \ln (x)} d x) + 4 (- e^{x \ln (x)} d x \ln (x^{3})) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.3.5

Multiplique $x^{2}$ por $x^{2}$ somando os expoentes.

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Etapa 14.4.1.3.5.1

Mova $x^{2}$ .

$\frac{- x^{2} d - 3 x^{x + 2} d + 3 (x^{2} x^{2}) d + x^{2} (- 3 e^{x \ln (x)} d x) + x^{2} (- e^{x \ln (x)} d x \ln (x^{3})) + x^{2} (4 d x) - 4 x (- d) - 4 x (- 3 x^{x} d) - 4 x (3 x^{2} d) - 4 x (- 3 e^{x \ln (x)} d x) - 4 x (- e^{x \ln (x)} d x \ln (x^{3})) - 4 x (4 d x) + 4 (- d) + 4 (- 3 x^{x} d) + 4 (3 x^{2} d) + 4 (- 3 e^{x \ln (x)} d x) + 4 (- e^{x \ln (x)} d x \ln (x^{3})) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.3.5.2

Use a regra da multiplicação de potências $a^{m} a^{n} = a^{m + n}$ para combinar expoentes.

$\frac{- x^{2} d - 3 x^{x + 2} d + 3 x^{2 + 2} d + x^{2} (- 3 e^{x \ln (x)} d x) + x^{2} (- e^{x \ln (x)} d x \ln (x^{3})) + x^{2} (4 d x) - 4 x (- d) - 4 x (- 3 x^{x} d) - 4 x (3 x^{2} d) - 4 x (- 3 e^{x \ln (x)} d x) - 4 x (- e^{x \ln (x)} d x \ln (x^{3})) - 4 x (4 d x) + 4 (- d) + 4 (- 3 x^{x} d) + 4 (3 x^{2} d) + 4 (- 3 e^{x \ln (x)} d x) + 4 (- e^{x \ln (x)} d x \ln (x^{3})) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.3.5.3

Some $2$ e $2$ .

$\frac{- x^{2} d - 3 x^{x + 2} d + 3 x^{4} d + x^{2} (- 3 e^{x \ln (x)} d x) + x^{2} (- e^{x \ln (x)} d x \ln (x^{3})) + x^{2} (4 d x) - 4 x (- d) - 4 x (- 3 x^{x} d) - 4 x (3 x^{2} d) - 4 x (- 3 e^{x \ln (x)} d x) - 4 x (- e^{x \ln (x)} d x \ln (x^{3})) - 4 x (4 d x) + 4 (- d) + 4 (- 3 x^{x} d) + 4 (3 x^{2} d) + 4 (- 3 e^{x \ln (x)} d x) + 4 (- e^{x \ln (x)} d x \ln (x^{3})) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.3.6

Reescreva usando a propriedade comutativa da multiplicação.

$\frac{- x^{2} d - 3 x^{x + 2} d + 3 x^{4} d - 3 x^{2} (e^{x \ln (x)} d x) + x^{2} (- e^{x \ln (x)} d x \ln (x^{3})) + x^{2} (4 d x) - 4 x (- d) - 4 x (- 3 x^{x} d) - 4 x (3 x^{2} d) - 4 x (- 3 e^{x \ln (x)} d x) - 4 x (- e^{x \ln (x)} d x \ln (x^{3})) - 4 x (4 d x) + 4 (- d) + 4 (- 3 x^{x} d) + 4 (3 x^{2} d) + 4 (- 3 e^{x \ln (x)} d x) + 4 (- e^{x \ln (x)} d x \ln (x^{3})) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.3.7

Multiplique $x^{2}$ por $x$ somando os expoentes.

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Etapa 14.4.1.3.7.1

Mova $x$ .

$\frac{- x^{2} d - 3 x^{x + 2} d + 3 x^{4} d - 3 (x \cdot x^{2}) (e^{x \ln (x)} d) + x^{2} (- e^{x \ln (x)} d x \ln (x^{3})) + x^{2} (4 d x) - 4 x (- d) - 4 x (- 3 x^{x} d) - 4 x (3 x^{2} d) - 4 x (- 3 e^{x \ln (x)} d x) - 4 x (- e^{x \ln (x)} d x \ln (x^{3})) - 4 x (4 d x) + 4 (- d) + 4 (- 3 x^{x} d) + 4 (3 x^{2} d) + 4 (- 3 e^{x \ln (x)} d x) + 4 (- e^{x \ln (x)} d x \ln (x^{3})) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.3.7.2

Multiplique $x$ por $x^{2}$ .

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Etapa 14.4.1.3.7.2.1

Eleve $x$ à potência de $1$ .

$\frac{- x^{2} d - 3 x^{x + 2} d + 3 x^{4} d - 3 (x^{1} x^{2}) (e^{x \ln (x)} d) + x^{2} (- e^{x \ln (x)} d x \ln (x^{3})) + x^{2} (4 d x) - 4 x (- d) - 4 x (- 3 x^{x} d) - 4 x (3 x^{2} d) - 4 x (- 3 e^{x \ln (x)} d x) - 4 x (- e^{x \ln (x)} d x \ln (x^{3})) - 4 x (4 d x) + 4 (- d) + 4 (- 3 x^{x} d) + 4 (3 x^{2} d) + 4 (- 3 e^{x \ln (x)} d x) + 4 (- e^{x \ln (x)} d x \ln (x^{3})) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.3.7.2.2

Use a regra da multiplicação de potências $a^{m} a^{n} = a^{m + n}$ para combinar expoentes.

$\frac{- x^{2} d - 3 x^{x + 2} d + 3 x^{4} d - 3 x^{1 + 2} (e^{x \ln (x)} d) + x^{2} (- e^{x \ln (x)} d x \ln (x^{3})) + x^{2} (4 d x) - 4 x (- d) - 4 x (- 3 x^{x} d) - 4 x (3 x^{2} d) - 4 x (- 3 e^{x \ln (x)} d x) - 4 x (- e^{x \ln (x)} d x \ln (x^{3})) - 4 x (4 d x) + 4 (- d) + 4 (- 3 x^{x} d) + 4 (3 x^{2} d) + 4 (- 3 e^{x \ln (x)} d x) + 4 (- e^{x \ln (x)} d x \ln (x^{3})) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.3.7.3

Some $1$ e $2$ .

$\frac{- x^{2} d - 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) + x^{2} (- e^{x \ln (x)} d x \ln (x^{3})) + x^{2} (4 d x) - 4 x (- d) - 4 x (- 3 x^{x} d) - 4 x (3 x^{2} d) - 4 x (- 3 e^{x \ln (x)} d x) - 4 x (- e^{x \ln (x)} d x \ln (x^{3})) - 4 x (4 d x) + 4 (- d) + 4 (- 3 x^{x} d) + 4 (3 x^{2} d) + 4 (- 3 e^{x \ln (x)} d x) + 4 (- e^{x \ln (x)} d x \ln (x^{3})) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.3.8

Reescreva usando a propriedade comutativa da multiplicação.

$\frac{- x^{2} d - 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{2} (e^{x \ln (x)} d x \ln (x^{3})) + x^{2} (4 d x) - 4 x (- d) - 4 x (- 3 x^{x} d) - 4 x (3 x^{2} d) - 4 x (- 3 e^{x \ln (x)} d x) - 4 x (- e^{x \ln (x)} d x \ln (x^{3})) - 4 x (4 d x) + 4 (- d) + 4 (- 3 x^{x} d) + 4 (3 x^{2} d) + 4 (- 3 e^{x \ln (x)} d x) + 4 (- e^{x \ln (x)} d x \ln (x^{3})) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.3.9

Multiplique $x^{2}$ por $x$ somando os expoentes.

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Etapa 14.4.1.3.9.1

Mova $x$ .

$\frac{- x^{2} d - 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - (x \cdot x^{2}) (e^{x \ln (x)} d \ln (x^{3})) + x^{2} (4 d x) - 4 x (- d) - 4 x (- 3 x^{x} d) - 4 x (3 x^{2} d) - 4 x (- 3 e^{x \ln (x)} d x) - 4 x (- e^{x \ln (x)} d x \ln (x^{3})) - 4 x (4 d x) + 4 (- d) + 4 (- 3 x^{x} d) + 4 (3 x^{2} d) + 4 (- 3 e^{x \ln (x)} d x) + 4 (- e^{x \ln (x)} d x \ln (x^{3})) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.3.9.2

Multiplique $x$ por $x^{2}$ .

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Etapa 14.4.1.3.9.2.1

Eleve $x$ à potência de $1$ .

$\frac{- x^{2} d - 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - (x^{1} x^{2}) (e^{x \ln (x)} d \ln (x^{3})) + x^{2} (4 d x) - 4 x (- d) - 4 x (- 3 x^{x} d) - 4 x (3 x^{2} d) - 4 x (- 3 e^{x \ln (x)} d x) - 4 x (- e^{x \ln (x)} d x \ln (x^{3})) - 4 x (4 d x) + 4 (- d) + 4 (- 3 x^{x} d) + 4 (3 x^{2} d) + 4 (- 3 e^{x \ln (x)} d x) + 4 (- e^{x \ln (x)} d x \ln (x^{3})) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.3.9.2.2

Use a regra da multiplicação de potências $a^{m} a^{n} = a^{m + n}$ para combinar expoentes.

$\frac{- x^{2} d - 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{1 + 2} (e^{x \ln (x)} d \ln (x^{3})) + x^{2} (4 d x) - 4 x (- d) - 4 x (- 3 x^{x} d) - 4 x (3 x^{2} d) - 4 x (- 3 e^{x \ln (x)} d x) - 4 x (- e^{x \ln (x)} d x \ln (x^{3})) - 4 x (4 d x) + 4 (- d) + 4 (- 3 x^{x} d) + 4 (3 x^{2} d) + 4 (- 3 e^{x \ln (x)} d x) + 4 (- e^{x \ln (x)} d x \ln (x^{3})) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.3.9.3

Some $1$ e $2$ .

$\frac{- x^{2} d - 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) + x^{2} (4 d x) - 4 x (- d) - 4 x (- 3 x^{x} d) - 4 x (3 x^{2} d) - 4 x (- 3 e^{x \ln (x)} d x) - 4 x (- e^{x \ln (x)} d x \ln (x^{3})) - 4 x (4 d x) + 4 (- d) + 4 (- 3 x^{x} d) + 4 (3 x^{2} d) + 4 (- 3 e^{x \ln (x)} d x) + 4 (- e^{x \ln (x)} d x \ln (x^{3})) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.3.10

Reescreva usando a propriedade comutativa da multiplicação.

$\frac{- x^{2} d - 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) + 4 x^{2} (d x) - 4 x (- d) - 4 x (- 3 x^{x} d) - 4 x (3 x^{2} d) - 4 x (- 3 e^{x \ln (x)} d x) - 4 x (- e^{x \ln (x)} d x \ln (x^{3})) - 4 x (4 d x) + 4 (- d) + 4 (- 3 x^{x} d) + 4 (3 x^{2} d) + 4 (- 3 e^{x \ln (x)} d x) + 4 (- e^{x \ln (x)} d x \ln (x^{3})) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.3.11

Multiplique $x^{2}$ por $x$ somando os expoentes.

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Etapa 14.4.1.3.11.1

Mova $x$ .

$\frac{- x^{2} d - 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) + 4 (x \cdot x^{2}) d - 4 x (- d) - 4 x (- 3 x^{x} d) - 4 x (3 x^{2} d) - 4 x (- 3 e^{x \ln (x)} d x) - 4 x (- e^{x \ln (x)} d x \ln (x^{3})) - 4 x (4 d x) + 4 (- d) + 4 (- 3 x^{x} d) + 4 (3 x^{2} d) + 4 (- 3 e^{x \ln (x)} d x) + 4 (- e^{x \ln (x)} d x \ln (x^{3})) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.3.11.2

Multiplique $x$ por $x^{2}$ .

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Etapa 14.4.1.3.11.2.1

Eleve $x$ à potência de $1$ .

$\frac{- x^{2} d - 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) + 4 (x^{1} x^{2}) d - 4 x (- d) - 4 x (- 3 x^{x} d) - 4 x (3 x^{2} d) - 4 x (- 3 e^{x \ln (x)} d x) - 4 x (- e^{x \ln (x)} d x \ln (x^{3})) - 4 x (4 d x) + 4 (- d) + 4 (- 3 x^{x} d) + 4 (3 x^{2} d) + 4 (- 3 e^{x \ln (x)} d x) + 4 (- e^{x \ln (x)} d x \ln (x^{3})) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.3.11.2.2

Use a regra da multiplicação de potências $a^{m} a^{n} = a^{m + n}$ para combinar expoentes.

$\frac{- x^{2} d - 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) + 4 x^{1 + 2} d - 4 x (- d) - 4 x (- 3 x^{x} d) - 4 x (3 x^{2} d) - 4 x (- 3 e^{x \ln (x)} d x) - 4 x (- e^{x \ln (x)} d x \ln (x^{3})) - 4 x (4 d x) + 4 (- d) + 4 (- 3 x^{x} d) + 4 (3 x^{2} d) + 4 (- 3 e^{x \ln (x)} d x) + 4 (- e^{x \ln (x)} d x \ln (x^{3})) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.3.11.3

Some $1$ e $2$ .

$\frac{- x^{2} d - 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) + 4 x^{3} d - 4 x (- d) - 4 x (- 3 x^{x} d) - 4 x (3 x^{2} d) - 4 x (- 3 e^{x \ln (x)} d x) - 4 x (- e^{x \ln (x)} d x \ln (x^{3})) - 4 x (4 d x) + 4 (- d) + 4 (- 3 x^{x} d) + 4 (3 x^{2} d) + 4 (- 3 e^{x \ln (x)} d x) + 4 (- e^{x \ln (x)} d x \ln (x^{3})) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.3.12

Reescreva usando a propriedade comutativa da multiplicação.

$\frac{- x^{2} d - 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) + 4 x^{3} d - 4 \cdot - 1 x d - 4 x (- 3 x^{x} d) - 4 x (3 x^{2} d) - 4 x (- 3 e^{x \ln (x)} d x) - 4 x (- e^{x \ln (x)} d x \ln (x^{3})) - 4 x (4 d x) + 4 (- d) + 4 (- 3 x^{x} d) + 4 (3 x^{2} d) + 4 (- 3 e^{x \ln (x)} d x) + 4 (- e^{x \ln (x)} d x \ln (x^{3})) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.3.13

Multiplique $- 4$ por $- 1$ .

$\frac{- x^{2} d - 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) + 4 x^{3} d + 4 x d - 4 x (- 3 x^{x} d) - 4 x (3 x^{2} d) - 4 x (- 3 e^{x \ln (x)} d x) - 4 x (- e^{x \ln (x)} d x \ln (x^{3})) - 4 x (4 d x) + 4 (- d) + 4 (- 3 x^{x} d) + 4 (3 x^{2} d) + 4 (- 3 e^{x \ln (x)} d x) + 4 (- e^{x \ln (x)} d x \ln (x^{3})) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.3.14

Multiplique $x$ por $x^{x}$ somando os expoentes.

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Etapa 14.4.1.3.14.1

Mova $x^{x}$ .

$\frac{- x^{2} d - 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) + 4 x^{3} d + 4 x d - 4 (x^{x} x) (- 3 d) - 4 x (3 x^{2} d) - 4 x (- 3 e^{x \ln (x)} d x) - 4 x (- e^{x \ln (x)} d x \ln (x^{3})) - 4 x (4 d x) + 4 (- d) + 4 (- 3 x^{x} d) + 4 (3 x^{2} d) + 4 (- 3 e^{x \ln (x)} d x) + 4 (- e^{x \ln (x)} d x \ln (x^{3})) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.3.14.2

Multiplique $x^{x}$ por $x$ .

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Etapa 14.4.1.3.14.2.1

Eleve $x$ à potência de $1$ .

$\frac{- x^{2} d - 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) + 4 x^{3} d + 4 x d - 4 (x^{x} x^{1}) (- 3 d) - 4 x (3 x^{2} d) - 4 x (- 3 e^{x \ln (x)} d x) - 4 x (- e^{x \ln (x)} d x \ln (x^{3})) - 4 x (4 d x) + 4 (- d) + 4 (- 3 x^{x} d) + 4 (3 x^{2} d) + 4 (- 3 e^{x \ln (x)} d x) + 4 (- e^{x \ln (x)} d x \ln (x^{3})) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.3.14.2.2

Use a regra da multiplicação de potências $a^{m} a^{n} = a^{m + n}$ para combinar expoentes.

$\frac{- x^{2} d - 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) + 4 x^{3} d + 4 x d - 4 x^{x + 1} (- 3 d) - 4 x (3 x^{2} d) - 4 x (- 3 e^{x \ln (x)} d x) - 4 x (- e^{x \ln (x)} d x \ln (x^{3})) - 4 x (4 d x) + 4 (- d) + 4 (- 3 x^{x} d) + 4 (3 x^{2} d) + 4 (- 3 e^{x \ln (x)} d x) + 4 (- e^{x \ln (x)} d x \ln (x^{3})) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.3.15

Reescreva usando a propriedade comutativa da multiplicação.

$\frac{- x^{2} d - 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) + 4 x^{3} d + 4 x d - 4 \cdot - 3 x^{x + 1} d - 4 x (3 x^{2} d) - 4 x (- 3 e^{x \ln (x)} d x) - 4 x (- e^{x \ln (x)} d x \ln (x^{3})) - 4 x (4 d x) + 4 (- d) + 4 (- 3 x^{x} d) + 4 (3 x^{2} d) + 4 (- 3 e^{x \ln (x)} d x) + 4 (- e^{x \ln (x)} d x \ln (x^{3})) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.3.16

Multiplique $- 4$ por $- 3$ .

$\frac{- x^{2} d - 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) + 4 x^{3} d + 4 x d + 12 x^{x + 1} d - 4 x (3 x^{2} d) - 4 x (- 3 e^{x \ln (x)} d x) - 4 x (- e^{x \ln (x)} d x \ln (x^{3})) - 4 x (4 d x) + 4 (- d) + 4 (- 3 x^{x} d) + 4 (3 x^{2} d) + 4 (- 3 e^{x \ln (x)} d x) + 4 (- e^{x \ln (x)} d x \ln (x^{3})) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.3.17

Multiplique $x$ por $x^{2}$ somando os expoentes.

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Etapa 14.4.1.3.17.1

Mova $x^{2}$ .

$\frac{- x^{2} d - 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) + 4 x^{3} d + 4 x d + 12 x^{x + 1} d - 4 (x^{2} x) (3 d) - 4 x (- 3 e^{x \ln (x)} d x) - 4 x (- e^{x \ln (x)} d x \ln (x^{3})) - 4 x (4 d x) + 4 (- d) + 4 (- 3 x^{x} d) + 4 (3 x^{2} d) + 4 (- 3 e^{x \ln (x)} d x) + 4 (- e^{x \ln (x)} d x \ln (x^{3})) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.3.17.2

Multiplique $x^{2}$ por $x$ .

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Etapa 14.4.1.3.17.2.1

Eleve $x$ à potência de $1$ .

$\frac{- x^{2} d - 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) + 4 x^{3} d + 4 x d + 12 x^{x + 1} d - 4 (x^{2} x^{1}) (3 d) - 4 x (- 3 e^{x \ln (x)} d x) - 4 x (- e^{x \ln (x)} d x \ln (x^{3})) - 4 x (4 d x) + 4 (- d) + 4 (- 3 x^{x} d) + 4 (3 x^{2} d) + 4 (- 3 e^{x \ln (x)} d x) + 4 (- e^{x \ln (x)} d x \ln (x^{3})) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.3.17.2.2

Use a regra da multiplicação de potências $a^{m} a^{n} = a^{m + n}$ para combinar expoentes.

$\frac{- x^{2} d - 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) + 4 x^{3} d + 4 x d + 12 x^{x + 1} d - 4 x^{2 + 1} (3 d) - 4 x (- 3 e^{x \ln (x)} d x) - 4 x (- e^{x \ln (x)} d x \ln (x^{3})) - 4 x (4 d x) + 4 (- d) + 4 (- 3 x^{x} d) + 4 (3 x^{2} d) + 4 (- 3 e^{x \ln (x)} d x) + 4 (- e^{x \ln (x)} d x \ln (x^{3})) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.3.17.3

Some $2$ e $1$ .

$\frac{- x^{2} d - 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) + 4 x^{3} d + 4 x d + 12 x^{x + 1} d - 4 x^{3} (3 d) - 4 x (- 3 e^{x \ln (x)} d x) - 4 x (- e^{x \ln (x)} d x \ln (x^{3})) - 4 x (4 d x) + 4 (- d) + 4 (- 3 x^{x} d) + 4 (3 x^{2} d) + 4 (- 3 e^{x \ln (x)} d x) + 4 (- e^{x \ln (x)} d x \ln (x^{3})) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.3.18

Reescreva usando a propriedade comutativa da multiplicação.

$\frac{- x^{2} d - 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) + 4 x^{3} d + 4 x d + 12 x^{x + 1} d - 4 \cdot 3 x^{3} d - 4 x (- 3 e^{x \ln (x)} d x) - 4 x (- e^{x \ln (x)} d x \ln (x^{3})) - 4 x (4 d x) + 4 (- d) + 4 (- 3 x^{x} d) + 4 (3 x^{2} d) + 4 (- 3 e^{x \ln (x)} d x) + 4 (- e^{x \ln (x)} d x \ln (x^{3})) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.3.19

Multiplique $- 4$ por $3$ .

$\frac{- x^{2} d - 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) + 4 x^{3} d + 4 x d + 12 x^{x + 1} d - 12 x^{3} d - 4 x (- 3 e^{x \ln (x)} d x) - 4 x (- e^{x \ln (x)} d x \ln (x^{3})) - 4 x (4 d x) + 4 (- d) + 4 (- 3 x^{x} d) + 4 (3 x^{2} d) + 4 (- 3 e^{x \ln (x)} d x) + 4 (- e^{x \ln (x)} d x \ln (x^{3})) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.3.20

Multiplique $x$ por $x$ somando os expoentes.

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Etapa 14.4.1.3.20.1

Mova $x$ .

$\frac{- x^{2} d - 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) + 4 x^{3} d + 4 x d + 12 x^{x + 1} d - 12 x^{3} d - 4 (x \cdot x) (- 3 e^{x \ln (x)} d) - 4 x (- e^{x \ln (x)} d x \ln (x^{3})) - 4 x (4 d x) + 4 (- d) + 4 (- 3 x^{x} d) + 4 (3 x^{2} d) + 4 (- 3 e^{x \ln (x)} d x) + 4 (- e^{x \ln (x)} d x \ln (x^{3})) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.3.20.2

Multiplique $x$ por $x$ .

$\frac{- x^{2} d - 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) + 4 x^{3} d + 4 x d + 12 x^{x + 1} d - 12 x^{3} d - 4 x^{2} (- 3 e^{x \ln (x)} d) - 4 x (- e^{x \ln (x)} d x \ln (x^{3})) - 4 x (4 d x) + 4 (- d) + 4 (- 3 x^{x} d) + 4 (3 x^{2} d) + 4 (- 3 e^{x \ln (x)} d x) + 4 (- e^{x \ln (x)} d x \ln (x^{3})) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.3.21

Multiplique $- 3$ por $- 4$ .

$\frac{- x^{2} d - 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) + 4 x^{3} d + 4 x d + 12 x^{x + 1} d - 12 x^{3} d + 12 x^{2} (e^{x \ln (x)} d) - 4 x (- e^{x \ln (x)} d x \ln (x^{3})) - 4 x (4 d x) + 4 (- d) + 4 (- 3 x^{x} d) + 4 (3 x^{2} d) + 4 (- 3 e^{x \ln (x)} d x) + 4 (- e^{x \ln (x)} d x \ln (x^{3})) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.3.22

Multiplique $x$ por $x$ somando os expoentes.

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Etapa 14.4.1.3.22.1

Mova $x$ .

$\frac{- x^{2} d - 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) + 4 x^{3} d + 4 x d + 12 x^{x + 1} d - 12 x^{3} d + 12 x^{2} (e^{x \ln (x)} d) - 4 (x \cdot x) (- e^{x \ln (x)} d \ln (x^{3})) - 4 x (4 d x) + 4 (- d) + 4 (- 3 x^{x} d) + 4 (3 x^{2} d) + 4 (- 3 e^{x \ln (x)} d x) + 4 (- e^{x \ln (x)} d x \ln (x^{3})) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.3.22.2

Multiplique $x$ por $x$ .

$\frac{- x^{2} d - 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) + 4 x^{3} d + 4 x d + 12 x^{x + 1} d - 12 x^{3} d + 12 x^{2} (e^{x \ln (x)} d) - 4 x^{2} (- e^{x \ln (x)} d \ln (x^{3})) - 4 x (4 d x) + 4 (- d) + 4 (- 3 x^{x} d) + 4 (3 x^{2} d) + 4 (- 3 e^{x \ln (x)} d x) + 4 (- e^{x \ln (x)} d x \ln (x^{3})) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.3.23

Multiplique $- 4 x^{2} (- e^{x \ln (x)} d \ln (x^{3}))$ .

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Etapa 14.4.1.3.23.1

Multiplique $- 1$ por $- 4$ .

$\frac{- x^{2} d - 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) + 4 x^{3} d + 4 x d + 12 x^{x + 1} d - 12 x^{3} d + 12 x^{2} (e^{x \ln (x)} d) + 4 x^{2} (e^{x \ln (x)} d \ln (x^{3})) - 4 x (4 d x) + 4 (- d) + 4 (- 3 x^{x} d) + 4 (3 x^{2} d) + 4 (- 3 e^{x \ln (x)} d x) + 4 (- e^{x \ln (x)} d x \ln (x^{3})) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.3.23.2

Simplifique $4 \ln (x^{3})$ movendo $4$ para dentro do logaritmo.

$\frac{- x^{2} d - 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) + 4 x^{3} d + 4 x d + 12 x^{x + 1} d - 12 x^{3} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln ({(x^{3})}^{4})) - 4 x (4 d x) + 4 (- d) + 4 (- 3 x^{x} d) + 4 (3 x^{2} d) + 4 (- 3 e^{x \ln (x)} d x) + 4 (- e^{x \ln (x)} d x \ln (x^{3})) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.3.24

Multiplique os expoentes em ${(x^{3})}^{4}$ .

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Etapa 14.4.1.3.24.1

Aplique a regra da multiplicação de potências e multiplique os expoentes, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{- x^{2} d - 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) + 4 x^{3} d + 4 x d + 12 x^{x + 1} d - 12 x^{3} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{3 \cdot 4})) - 4 x (4 d x) + 4 (- d) + 4 (- 3 x^{x} d) + 4 (3 x^{2} d) + 4 (- 3 e^{x \ln (x)} d x) + 4 (- e^{x \ln (x)} d x \ln (x^{3})) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.3.24.2

Multiplique $3$ por $4$ .

$\frac{- x^{2} d - 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) + 4 x^{3} d + 4 x d + 12 x^{x + 1} d - 12 x^{3} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 4 x (4 d x) + 4 (- d) + 4 (- 3 x^{x} d) + 4 (3 x^{2} d) + 4 (- 3 e^{x \ln (x)} d x) + 4 (- e^{x \ln (x)} d x \ln (x^{3})) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.3.25

Multiplique $x$ por $x$ somando os expoentes.

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Etapa 14.4.1.3.25.1

Mova $x$ .

$\frac{- x^{2} d - 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) + 4 x^{3} d + 4 x d + 12 x^{x + 1} d - 12 x^{3} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 4 (x \cdot x) (4 d) + 4 (- d) + 4 (- 3 x^{x} d) + 4 (3 x^{2} d) + 4 (- 3 e^{x \ln (x)} d x) + 4 (- e^{x \ln (x)} d x \ln (x^{3})) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.3.25.2

Multiplique $x$ por $x$ .

$\frac{- x^{2} d - 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) + 4 x^{3} d + 4 x d + 12 x^{x + 1} d - 12 x^{3} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 4 x^{2} (4 d) + 4 (- d) + 4 (- 3 x^{x} d) + 4 (3 x^{2} d) + 4 (- 3 e^{x \ln (x)} d x) + 4 (- e^{x \ln (x)} d x \ln (x^{3})) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.3.26

Reescreva usando a propriedade comutativa da multiplicação.

$\frac{- x^{2} d - 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) + 4 x^{3} d + 4 x d + 12 x^{x + 1} d - 12 x^{3} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 4 \cdot 4 x^{2} d + 4 (- d) + 4 (- 3 x^{x} d) + 4 (3 x^{2} d) + 4 (- 3 e^{x \ln (x)} d x) + 4 (- e^{x \ln (x)} d x \ln (x^{3})) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.3.27

Multiplique $- 4$ por $4$ .

$\frac{- x^{2} d - 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) + 4 x^{3} d + 4 x d + 12 x^{x + 1} d - 12 x^{3} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 16 x^{2} d + 4 (- d) + 4 (- 3 x^{x} d) + 4 (3 x^{2} d) + 4 (- 3 e^{x \ln (x)} d x) + 4 (- e^{x \ln (x)} d x \ln (x^{3})) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.3.28

Multiplique $- 1$ por $4$ .

$\frac{- x^{2} d - 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) + 4 x^{3} d + 4 x d + 12 x^{x + 1} d - 12 x^{3} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 16 x^{2} d - 4 d + 4 (- 3 x^{x} d) + 4 (3 x^{2} d) + 4 (- 3 e^{x \ln (x)} d x) + 4 (- e^{x \ln (x)} d x \ln (x^{3})) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.3.29

Multiplique $- 3$ por $4$ .

$\frac{- x^{2} d - 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) + 4 x^{3} d + 4 x d + 12 x^{x + 1} d - 12 x^{3} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 16 x^{2} d - 4 d - 12 (x^{x} d) + 4 (3 x^{2} d) + 4 (- 3 e^{x \ln (x)} d x) + 4 (- e^{x \ln (x)} d x \ln (x^{3})) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.3.30

Multiplique $3$ por $4$ .

$\frac{- x^{2} d - 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) + 4 x^{3} d + 4 x d + 12 x^{x + 1} d - 12 x^{3} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 16 x^{2} d - 4 d - 12 x^{x} d + 12 (x^{2} d) + 4 (- 3 e^{x \ln (x)} d x) + 4 (- e^{x \ln (x)} d x \ln (x^{3})) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.3.31

Multiplique $- 3$ por $4$ .

$\frac{- x^{2} d - 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) + 4 x^{3} d + 4 x d + 12 x^{x + 1} d - 12 x^{3} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 16 x^{2} d - 4 d - 12 x^{x} d + 12 x^{2} d - 12 (e^{x \ln (x)} d x) + 4 (- e^{x \ln (x)} d x \ln (x^{3})) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.3.32

Multiplique $4 (- e^{x \ln (x)} d x \ln (x^{3}))$ .

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Etapa 14.4.1.3.32.1

Multiplique $- 1$ por $4$ .

$\frac{- x^{2} d - 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) + 4 x^{3} d + 4 x d + 12 x^{x + 1} d - 12 x^{3} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 16 x^{2} d - 4 d - 12 x^{x} d + 12 x^{2} d - 12 e^{x \ln (x)} d x - 4 (e^{x \ln (x)} d x \ln (x^{3})) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.3.32.2

Simplifique $- 4 \ln (x^{3})$ movendo $4$ para dentro do logaritmo.

$\frac{- x^{2} d - 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) + 4 x^{3} d + 4 x d + 12 x^{x + 1} d - 12 x^{3} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 16 x^{2} d - 4 d - 12 x^{x} d + 12 x^{2} d - 12 e^{x \ln (x)} d x + e^{x \ln (x)} d x (- \ln ({(x^{3})}^{4})) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.3.33

Reescreva usando a propriedade comutativa da multiplicação.

$\frac{- x^{2} d - 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) + 4 x^{3} d + 4 x d + 12 x^{x + 1} d - 12 x^{3} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 16 x^{2} d - 4 d - 12 x^{x} d + 12 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln ({(x^{3})}^{4}) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.3.34

Multiplique os expoentes em ${(x^{3})}^{4}$ .

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Etapa 14.4.1.3.34.1

Aplique a regra da multiplicação de potências e multiplique os expoentes, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{- x^{2} d - 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) + 4 x^{3} d + 4 x d + 12 x^{x + 1} d - 12 x^{3} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 16 x^{2} d - 4 d - 12 x^{x} d + 12 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{3 \cdot 4}) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.3.34.2

Multiplique $3$ por $4$ .

$\frac{- x^{2} d - 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) + 4 x^{3} d + 4 x d + 12 x^{x + 1} d - 12 x^{3} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 16 x^{2} d - 4 d - 12 x^{x} d + 12 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.3.35

Multiplique $4$ por $4$ .

$\frac{- x^{2} d - 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) + 4 x^{3} d + 4 x d + 12 x^{x + 1} d - 12 x^{3} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 16 x^{2} d - 4 d - 12 x^{x} d + 12 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 16 d x + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.4

Subtraia $16 x^{2} d$ de $- x^{2} d$ .

$\frac{- 17 x^{2} d - 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) + 4 x^{3} d + 4 x d + 12 x^{x + 1} d - 12 x^{3} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 4 d - 12 x^{x} d + 12 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 16 d x + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.5

Some $- 17 x^{2} d$ e $12 x^{2} d$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) + 4 x^{3} d + 4 x d + 12 x^{x + 1} d - 12 x^{3} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 4 d - 12 x^{x} d - 5 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 16 d x + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.6

Subtraia $12 x^{3} d$ de $4 x^{3} d$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 8 x^{3} d + 4 x d + 12 x^{x + 1} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 4 d - 12 x^{x} d - 5 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 16 d x + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.7

Some $4 x d$ e $16 d x$ .

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Etapa 14.4.1.7.1

Mova $x$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 8 x^{3} d + 12 x^{x + 1} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 4 d - 12 x^{x} d - 5 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 4 d x + 16 d x + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.7.2

Some $4 d x$ e $16 d x$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 8 x^{3} d + 12 x^{x + 1} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 4 d - 12 x^{x} d - 5 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 20 d x + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.8

Simplifique cada termo.

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Etapa 14.4.1.8.1

Multiplique $x^{2}$ por $x$ somando os expoentes.

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Etapa 14.4.1.8.1.1

Mova $x$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 8 x^{3} d + 12 x^{x + 1} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 4 d - 12 x^{x} d - 5 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 20 d x + (- (x \cdot x^{2}) d - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.8.1.2

Multiplique $x$ por $x^{2}$ .

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Etapa 14.4.1.8.1.2.1

Eleve $x$ à potência de $1$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 8 x^{3} d + 12 x^{x + 1} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 4 d - 12 x^{x} d - 5 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 20 d x + (- (x^{1} x^{2}) d - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.8.1.2.2

Use a regra da multiplicação de potências $a^{m} a^{n} = a^{m + n}$ para combinar expoentes.

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 8 x^{3} d + 12 x^{x + 1} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 4 d - 12 x^{x} d - 5 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 20 d x + (- x^{1 + 2} d - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.8.1.3

Some $1$ e $2$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 8 x^{3} d + 12 x^{x + 1} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 4 d - 12 x^{x} d - 5 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 20 d x + (- x^{3} d - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.8.2

Multiplique $x^{x}$ por $x$ somando os expoentes.

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Etapa 14.4.1.8.2.1

Mova $x$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 8 x^{3} d + 12 x^{x + 1} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 4 d - 12 x^{x} d - 5 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 20 d x + (- x^{3} d - (- 3 (x \cdot x^{x})) d - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.8.2.2

Multiplique $x$ por $x^{x}$ .

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Etapa 14.4.1.8.2.2.1

Eleve $x$ à potência de $1$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 8 x^{3} d + 12 x^{x + 1} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 4 d - 12 x^{x} d - 5 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 20 d x + (- x^{3} d - (- 3 (x^{1} x^{x})) d - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.8.2.2.2

Use a regra da multiplicação de potências $a^{m} a^{n} = a^{m + n}$ para combinar expoentes.

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 8 x^{3} d + 12 x^{x + 1} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 4 d - 12 x^{x} d - 5 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 20 d x + (- x^{3} d - (- 3 x^{1 + x}) d - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.8.3

Multiplique $- 3$ por $- 1$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 8 x^{3} d + 12 x^{x + 1} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 4 d - 12 x^{x} d - 5 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 20 d x + (- x^{3} d + 3 x^{1 + x} d - (2 x) d x - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.8.4

Multiplique $x$ por $x$ somando os expoentes.

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Etapa 14.4.1.8.4.1

Mova $x$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 8 x^{3} d + 12 x^{x + 1} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 4 d - 12 x^{x} d - 5 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 20 d x + (- x^{3} d + 3 x^{1 + x} d - (2 (x \cdot x)) d - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.8.4.2

Multiplique $x$ por $x$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 8 x^{3} d + 12 x^{x + 1} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 4 d - 12 x^{x} d - 5 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 20 d x + (- x^{3} d + 3 x^{1 + x} d - (2 x^{2}) d - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.8.5

Multiplique $2$ por $- 1$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 8 x^{3} d + 12 x^{x + 1} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 4 d - 12 x^{x} d - 5 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 20 d x + (- x^{3} d + 3 x^{1 + x} d - 2 x^{2} d - - 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.8.6

Multiplique $- 1$ por $- 1$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 8 x^{3} d + 12 x^{x + 1} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 4 d - 12 x^{x} d - 5 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 20 d x + (- x^{3} d + 3 x^{1 + x} d - 2 x^{2} d + 1 d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.8.7

Multiplique $d$ por $1$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 8 x^{3} d + 12 x^{x + 1} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 4 d - 12 x^{x} d - 5 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 20 d x + (- x^{3} d + 3 x^{1 + x} d - 2 x^{2} d + d x) (2 x - 4)}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.9

Expanda $(- x^{3} d + 3 x^{1 + x} d - 2 x^{2} d + d x) (2 x - 4)$ multiplicando cada termo na primeira expressão por cada um dos termos na segunda expressão.

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 8 x^{3} d + 12 x^{x + 1} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 4 d - 12 x^{x} d - 5 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 20 d x - x^{3} d (2 x) - x^{3} d \cdot - 4 + 3 x^{1 + x} d (2 x) + 3 x^{1 + x} d \cdot - 4 - 2 x^{2} d (2 x) - 2 x^{2} d \cdot - 4 + d x (2 x) + d x \cdot - 4}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.10

Simplifique cada termo.

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Etapa 14.4.1.10.1

Multiplique $x^{3}$ por $x$ somando os expoentes.

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Etapa 14.4.1.10.1.1

Mova $x$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 8 x^{3} d + 12 x^{x + 1} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 4 d - 12 x^{x} d - 5 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 20 d x - (x \cdot x^{3}) d \cdot 2 - x^{3} d \cdot - 4 + 3 x^{1 + x} d (2 x) + 3 x^{1 + x} d \cdot - 4 - 2 x^{2} d (2 x) - 2 x^{2} d \cdot - 4 + d x (2 x) + d x \cdot - 4}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.10.1.2

Multiplique $x$ por $x^{3}$ .

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Etapa 14.4.1.10.1.2.1

Eleve $x$ à potência de $1$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 8 x^{3} d + 12 x^{x + 1} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 4 d - 12 x^{x} d - 5 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 20 d x - (x^{1} x^{3}) d \cdot 2 - x^{3} d \cdot - 4 + 3 x^{1 + x} d (2 x) + 3 x^{1 + x} d \cdot - 4 - 2 x^{2} d (2 x) - 2 x^{2} d \cdot - 4 + d x (2 x) + d x \cdot - 4}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.10.1.2.2

Use a regra da multiplicação de potências $a^{m} a^{n} = a^{m + n}$ para combinar expoentes.

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 8 x^{3} d + 12 x^{x + 1} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 4 d - 12 x^{x} d - 5 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 20 d x - x^{1 + 3} d \cdot 2 - x^{3} d \cdot - 4 + 3 x^{1 + x} d (2 x) + 3 x^{1 + x} d \cdot - 4 - 2 x^{2} d (2 x) - 2 x^{2} d \cdot - 4 + d x (2 x) + d x \cdot - 4}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.10.1.3

Some $1$ e $3$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 8 x^{3} d + 12 x^{x + 1} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 4 d - 12 x^{x} d - 5 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 20 d x - x^{4} d \cdot 2 - x^{3} d \cdot - 4 + 3 x^{1 + x} d (2 x) + 3 x^{1 + x} d \cdot - 4 - 2 x^{2} d (2 x) - 2 x^{2} d \cdot - 4 + d x (2 x) + d x \cdot - 4}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.10.2

Multiplique $2$ por $- 1$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 8 x^{3} d + 12 x^{x + 1} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 4 d - 12 x^{x} d - 5 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 20 d x - 2 x^{4} d - x^{3} d \cdot - 4 + 3 x^{1 + x} d (2 x) + 3 x^{1 + x} d \cdot - 4 - 2 x^{2} d (2 x) - 2 x^{2} d \cdot - 4 + d x (2 x) + d x \cdot - 4}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.10.3

Multiplique $- 4$ por $- 1$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 8 x^{3} d + 12 x^{x + 1} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 4 d - 12 x^{x} d - 5 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 20 d x - 2 x^{4} d + 4 x^{3} d + 3 x^{1 + x} d (2 x) + 3 x^{1 + x} d \cdot - 4 - 2 x^{2} d (2 x) - 2 x^{2} d \cdot - 4 + d x (2 x) + d x \cdot - 4}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.10.4

Multiplique $x^{1 + x}$ por $x$ somando os expoentes.

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Etapa 14.4.1.10.4.1

Mova $x$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 8 x^{3} d + 12 x^{x + 1} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 4 d - 12 x^{x} d - 5 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 20 d x - 2 x^{4} d + 4 x^{3} d + 3 (x \cdot x^{1 + x}) d \cdot 2 + 3 x^{1 + x} d \cdot - 4 - 2 x^{2} d (2 x) - 2 x^{2} d \cdot - 4 + d x (2 x) + d x \cdot - 4}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.10.4.2

Multiplique $x$ por $x^{1 + x}$ .

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Etapa 14.4.1.10.4.2.1

Eleve $x$ à potência de $1$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 8 x^{3} d + 12 x^{x + 1} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 4 d - 12 x^{x} d - 5 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 20 d x - 2 x^{4} d + 4 x^{3} d + 3 (x^{1} x^{1 + x}) d \cdot 2 + 3 x^{1 + x} d \cdot - 4 - 2 x^{2} d (2 x) - 2 x^{2} d \cdot - 4 + d x (2 x) + d x \cdot - 4}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.10.4.2.2

Use a regra da multiplicação de potências $a^{m} a^{n} = a^{m + n}$ para combinar expoentes.

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 8 x^{3} d + 12 x^{x + 1} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 4 d - 12 x^{x} d - 5 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 20 d x - 2 x^{4} d + 4 x^{3} d + 3 x^{1 + 1 + x} d \cdot 2 + 3 x^{1 + x} d \cdot - 4 - 2 x^{2} d (2 x) - 2 x^{2} d \cdot - 4 + d x (2 x) + d x \cdot - 4}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.10.4.3

Some $1$ e $1$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 8 x^{3} d + 12 x^{x + 1} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 4 d - 12 x^{x} d - 5 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 20 d x - 2 x^{4} d + 4 x^{3} d + 3 x^{2 + x} d \cdot 2 + 3 x^{1 + x} d \cdot - 4 - 2 x^{2} d (2 x) - 2 x^{2} d \cdot - 4 + d x (2 x) + d x \cdot - 4}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.10.5

Multiplique $2$ por $3$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 8 x^{3} d + 12 x^{x + 1} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 4 d - 12 x^{x} d - 5 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 20 d x - 2 x^{4} d + 4 x^{3} d + 6 x^{2 + x} d + 3 x^{1 + x} d \cdot - 4 - 2 x^{2} d (2 x) - 2 x^{2} d \cdot - 4 + d x (2 x) + d x \cdot - 4}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.10.6

Multiplique $- 4$ por $3$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 8 x^{3} d + 12 x^{x + 1} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 4 d - 12 x^{x} d - 5 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 20 d x - 2 x^{4} d + 4 x^{3} d + 6 x^{2 + x} d - 12 x^{1 + x} d - 2 x^{2} d (2 x) - 2 x^{2} d \cdot - 4 + d x (2 x) + d x \cdot - 4}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.10.7

Multiplique $x^{2}$ por $x$ somando os expoentes.

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Etapa 14.4.1.10.7.1

Mova $x$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 8 x^{3} d + 12 x^{x + 1} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 4 d - 12 x^{x} d - 5 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 20 d x - 2 x^{4} d + 4 x^{3} d + 6 x^{2 + x} d - 12 x^{1 + x} d - 2 (x \cdot x^{2}) d \cdot 2 - 2 x^{2} d \cdot - 4 + d x (2 x) + d x \cdot - 4}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.10.7.2

Multiplique $x$ por $x^{2}$ .

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Etapa 14.4.1.10.7.2.1

Eleve $x$ à potência de $1$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 8 x^{3} d + 12 x^{x + 1} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 4 d - 12 x^{x} d - 5 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 20 d x - 2 x^{4} d + 4 x^{3} d + 6 x^{2 + x} d - 12 x^{1 + x} d - 2 (x^{1} x^{2}) d \cdot 2 - 2 x^{2} d \cdot - 4 + d x (2 x) + d x \cdot - 4}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.10.7.2.2

Use a regra da multiplicação de potências $a^{m} a^{n} = a^{m + n}$ para combinar expoentes.

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 8 x^{3} d + 12 x^{x + 1} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 4 d - 12 x^{x} d - 5 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 20 d x - 2 x^{4} d + 4 x^{3} d + 6 x^{2 + x} d - 12 x^{1 + x} d - 2 x^{1 + 2} d \cdot 2 - 2 x^{2} d \cdot - 4 + d x (2 x) + d x \cdot - 4}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.10.7.3

Some $1$ e $2$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 8 x^{3} d + 12 x^{x + 1} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 4 d - 12 x^{x} d - 5 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 20 d x - 2 x^{4} d + 4 x^{3} d + 6 x^{2 + x} d - 12 x^{1 + x} d - 2 x^{3} d \cdot 2 - 2 x^{2} d \cdot - 4 + d x (2 x) + d x \cdot - 4}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.10.8

Multiplique $2$ por $- 2$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 8 x^{3} d + 12 x^{x + 1} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 4 d - 12 x^{x} d - 5 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 20 d x - 2 x^{4} d + 4 x^{3} d + 6 x^{2 + x} d - 12 x^{1 + x} d - 4 x^{3} d - 2 x^{2} d \cdot - 4 + d x (2 x) + d x \cdot - 4}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.10.9

Multiplique $- 4$ por $- 2$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 8 x^{3} d + 12 x^{x + 1} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 4 d - 12 x^{x} d - 5 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 20 d x - 2 x^{4} d + 4 x^{3} d + 6 x^{2 + x} d - 12 x^{1 + x} d - 4 x^{3} d + 8 x^{2} d + d x (2 x) + d x \cdot - 4}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.10.10

Reescreva usando a propriedade comutativa da multiplicação.

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 8 x^{3} d + 12 x^{x + 1} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 4 d - 12 x^{x} d - 5 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 20 d x - 2 x^{4} d + 4 x^{3} d + 6 x^{2 + x} d - 12 x^{1 + x} d - 4 x^{3} d + 8 x^{2} d + 2 d x \cdot x + d x \cdot - 4}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.10.11

Multiplique $x$ por $x$ somando os expoentes.

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Etapa 14.4.1.10.11.1

Mova $x$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 8 x^{3} d + 12 x^{x + 1} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 4 d - 12 x^{x} d - 5 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 20 d x - 2 x^{4} d + 4 x^{3} d + 6 x^{2 + x} d - 12 x^{1 + x} d - 4 x^{3} d + 8 x^{2} d + 2 d (x \cdot x) + d x \cdot - 4}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.10.11.2

Multiplique $x$ por $x$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 8 x^{3} d + 12 x^{x + 1} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 4 d - 12 x^{x} d - 5 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 20 d x - 2 x^{4} d + 4 x^{3} d + 6 x^{2 + x} d - 12 x^{1 + x} d - 4 x^{3} d + 8 x^{2} d + 2 d x^{2} + d x \cdot - 4}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.10.12

Mova $- 4$ para a esquerda de $d x$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 8 x^{3} d + 12 x^{x + 1} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 4 d - 12 x^{x} d - 5 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 20 d x - 2 x^{4} d + 4 x^{3} d + 6 x^{2 + x} d - 12 x^{1 + x} d - 4 x^{3} d + 8 x^{2} d + 2 d x^{2} - 4 d x}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.11

Combine os termos opostos em $- 2 x^{4} d + 4 x^{3} d + 6 x^{2 + x} d - 12 x^{1 + x} d - 4 x^{3} d + 8 x^{2} d + 2 d x^{2} - 4 d x$ .

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Etapa 14.4.1.11.1

Subtraia $4 x^{3} d$ de $4 x^{3} d$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 8 x^{3} d + 12 x^{x + 1} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 4 d - 12 x^{x} d - 5 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 20 d x - 2 x^{4} d + 6 x^{2 + x} d - 12 x^{1 + x} d + 0 + 8 x^{2} d + 2 d x^{2} - 4 d x}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.11.2

Some $- 2 x^{4} d + 6 x^{2 + x} d - 12 x^{1 + x} d$ e $0$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 8 x^{3} d + 12 x^{x + 1} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 4 d - 12 x^{x} d - 5 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 20 d x - 2 x^{4} d + 6 x^{2 + x} d - 12 x^{1 + x} d + 8 x^{2} d + 2 d x^{2} - 4 d x}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.12

Some $8 x^{2} d$ e $2 d x^{2}$ .

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Etapa 14.4.1.12.1

Mova $x^{2}$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 8 x^{3} d + 12 x^{x + 1} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 4 d - 12 x^{x} d - 5 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 20 d x - 2 x^{4} d + 6 x^{2 + x} d - 12 x^{1 + x} d + 8 d x^{2} + 2 d x^{2} - 4 d x}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.1.12.2

Some $8 d x^{2}$ e $2 d x^{2}$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 8 x^{3} d + 12 x^{x + 1} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 4 d - 12 x^{x} d - 5 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 20 d x - 2 x^{4} d + 6 x^{2 + x} d - 12 x^{1 + x} d + 10 d x^{2} - 4 d x}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.2

Mova $x^{x + 2}$ .

$\frac{3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 8 x^{3} d + 12 x^{x + 1} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 4 d - 12 x^{x} d - 5 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 20 d x - 2 x^{4} d - 3 d x^{x + 2} + 6 d x^{x + 2} - 12 x^{1 + x} d + 10 d x^{2} - 4 d x}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.3

Subtraia $2 x^{4} d$ de $3 x^{4} d$ .

$\frac{- 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 8 x^{3} d + 12 x^{x + 1} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 4 d - 12 x^{x} d - 5 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 20 d x + 1 x^{4} d - 3 d x^{x + 2} + 6 d x^{x + 2} - 12 x^{1 + x} d + 10 d x^{2} - 4 d x}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.4

Multiplique $x^{4}$ por $1$ .

$\frac{- 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 8 x^{3} d + 12 x^{x + 1} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 4 d - 12 x^{x} d - 5 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 20 d x + x^{4} d - 3 d x^{x + 2} + 6 d x^{x + 2} - 12 x^{1 + x} d + 10 d x^{2} - 4 d x}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.5

Mova $x^{x + 1}$ .

$\frac{- 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 8 x^{3} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 4 d - 12 x^{x} d - 5 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 20 d x + x^{4} d - 3 d x^{x + 2} + 6 d x^{x + 2} + 12 d x^{x + 1} - 12 d x^{x + 1} + 10 d x^{2} - 4 d x}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.6

Combine os termos opostos em $- 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 8 x^{3} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 4 d - 12 x^{x} d - 5 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 20 d x + x^{4} d - 3 d x^{x + 2} + 6 d x^{x + 2} + 12 d x^{x + 1} - 12 d x^{x + 1} + 10 d x^{2} - 4 d x$ .

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Etapa 14.4.6.1

Subtraia $12 d x^{x + 1}$ de $12 d x^{x + 1}$ .

Etapa 14.4.6.2

Some $- 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 8 x^{3} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 4 d - 12 x^{x} d - 5 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 20 d x + x^{4} d - 3 d x^{x + 2} + 6 d x^{x + 2}$ e $0$ .

Etapa 14.4.7

Some $- 5 x^{2} d$ e $10 d x^{2}$ .

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Etapa 14.4.7.1

Mova $x^{2}$ .

$\frac{- 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 8 x^{3} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 4 d - 12 x^{x} d - 5 d x^{2} + 10 d x^{2} - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 20 d x + x^{4} d - 3 d x^{x + 2} + 6 d x^{x + 2} - 4 d x}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.7.2

Some $- 5 d x^{2}$ e $10 d x^{2}$ .

$\frac{- 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 8 x^{3} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 4 d - 12 x^{x} d + 5 d x^{2} - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 20 d x + x^{4} d - 3 d x^{x + 2} + 6 d x^{x + 2} - 4 d x}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.8

Subtraia $4 d x$ de $20 d x$ .

$\frac{- 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 8 x^{3} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 4 d - 12 x^{x} d + 5 d x^{2} - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 16 d x + x^{4} d - 3 d x^{x + 2} + 6 d x^{x + 2}}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.9

Some $- 3 d x^{x + 2}$ e $6 d x^{x + 2}$ .

$\frac{- 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 8 x^{3} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 4 d - 12 x^{x} d + 5 d x^{2} - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 16 d x + x^{4} d + 3 d x^{x + 2}}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.4.10

Reordene os fatores em $- 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 8 x^{3} d + 12 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{12})) - 4 d - 12 x^{x} d + 5 d x^{2} - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 16 d x + x^{4} d + 3 d x^{x + 2}$ .

$\frac{- 3 x^{3} d e^{x \ln (x)} - x^{3} d e^{x \ln (x)} \ln (x^{3}) - 8 x^{3} d + 12 x^{2} d e^{x \ln (x)} + x^{2} d e^{x \ln (x)} \ln (x^{12}) - 4 d - 12 d x^{x} + 5 d x^{2} - 12 d x e^{x \ln (x)} - d x e^{x \ln (x)} \ln (x^{12}) + 16 d x + x^{4} d + 3 d x^{x + 2}}{{(x^{2} - 4 x + 4)}^{2}}$

Etapa 14.5

Reordene os termos.

$\frac{- 4 d - 3 e^{x \ln (x)} x^{3} d - e^{x \ln (x)} x^{3} d \ln (x^{3}) - 8 x^{3} d + 12 e^{x \ln (x)} x^{2} d + e^{x \ln (x)} x^{2} d \ln (x^{12}) - 12 x^{x} d + 5 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 16 d x + x^{4} d + 3 x^{x + 2} d}{{(x^{2} - 4 x + 4)}^{2}}$