Cálculo Ejemplos

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

Paso 1

Diferencia con la regla del cociente, que establece que $\frac{d}{d x} [\frac{f (x)}{g (x)}]$ es $\frac{g (x) \frac{d}{d x} [f (x)] - f (x) \frac{d}{d x} [g (x)]}{{g (x)}^{2}}$ donde $f (x) = (x^{2} - 3 x^{x} + 2 x - 1) d x$ y $g (x) = x^{2} - 6 x + 4$ .

$\frac{(x^{2} - 6 x + 4) \frac{d}{d x} [(x^{2} - 3 x^{x} + 2 x - 1) d x] - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 6 x + 4]}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 2

Como $d$ es constante con respecto a $x$ , la derivada de $(x^{2} - 3 x^{x} + 2 x - 1) d x$ con respecto a $x$ es $d \frac{d}{d x} [(x^{2} - 3 x^{x} + 2 x - 1) x]$ .

$\frac{(x^{2} - 6 x + 4) (d \frac{d}{d x} [(x^{2} - 3 x^{x} + 2 x - 1) x]) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 6 x + 4]}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 3

Diferencia con la regla del producto, que establece que $\frac{d}{d x} [f (x) g (x)]$ es $f (x) \frac{d}{d x} [g (x)] + g (x) \frac{d}{d x} [f (x)]$ donde $f (x) = x^{2} - 3 x^{x} + 2 x - 1$ y $g (x) = x$ .

$\frac{(x^{2} - 6 x + 4) (d ((x^{2} - 3 x^{x} + 2 x - 1) \frac{d}{d x} [x] + x \frac{d}{d x} [x^{2} - 3 x^{x} + 2 x - 1])) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 6 x + 4]}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 4

Diferencia.

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Paso 4.1

Diferencia con la regla de la potencia, que establece que $\frac{d}{d x} [x^{n}]$ es $n x^{n - 1}$ donde $n = 1$ .

$\frac{(x^{2} - 6 x + 4) (d ((x^{2} - 3 x^{x} + 2 x - 1) \cdot 1 + x \frac{d}{d x} [x^{2} - 3 x^{x} + 2 x - 1])) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 6 x + 4]}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 4.2

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

$\frac{(x^{2} - 6 x + 4) (d (x^{2} - 3 x^{x} + 2 x - 1 + x \frac{d}{d x} [x^{2} - 3 x^{x} + 2 x - 1])) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 6 x + 4]}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 4.3

Según la regla de la suma, la derivada de $x^{2} - 3 x^{x} + 2 x - 1$ con respecto a $x$ es $\frac{d}{d x} [x^{2}] + \frac{d}{d x} [- 3 x^{x}] + \frac{d}{d x} [2 x] + \frac{d}{d x} [- 1]$ .

$\frac{(x^{2} - 6 x + 4) (d (x^{2} - 3 x^{x} + 2 x - 1 + x (\frac{d}{d x} [x^{2}] + \frac{d}{d x} [- 3 x^{x}] + \frac{d}{d x} [2 x] + \frac{d}{d x} [- 1]))) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 6 x + 4]}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 4.4

Diferencia con la regla de la potencia, que establece que $\frac{d}{d x} [x^{n}]$ es $n x^{n - 1}$ donde $n = 2$ .

$\frac{(x^{2} - 6 x + 4) (d (x^{2} - 3 x^{x} + 2 x - 1 + x (2 x + \frac{d}{d x} [- 3 x^{x}] + \frac{d}{d x} [2 x] + \frac{d}{d x} [- 1]))) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 6 x + 4]}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 4.5

Como $- 3$ es constante con respecto a $x$ , la derivada de $- 3 x^{x}$ con respecto a $x$ es $- 3 \frac{d}{d x} [x^{x}]$ .

$\frac{(x^{2} - 6 x + 4) (d (x^{2} - 3 x^{x} + 2 x - 1 + x (2 x - 3 \frac{d}{d x} [x^{x}] + \frac{d}{d x} [2 x] + \frac{d}{d x} [- 1]))) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 6 x + 4]}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 5

Usa las propiedades de los logaritmos para simplificar la diferenciación.

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Paso 5.1

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

$\frac{(x^{2} - 6 x + 4) (d (x^{2} - 3 x^{x} + 2 x - 1 + x (2 x - 3 \frac{d}{d x} [e^{\ln (x^{x})}] + \frac{d}{d x} [2 x] + \frac{d}{d x} [- 1]))) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 6 x + 4]}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 5.2

Expande $\ln (x^{x})$ ; para ello, mueve $x$ fuera del logaritmo.

$\frac{(x^{2} - 6 x + 4) (d (x^{2} - 3 x^{x} + 2 x - 1 + x (2 x - 3 \frac{d}{d x} [e^{x \ln (x)}] + \frac{d}{d x} [2 x] + \frac{d}{d x} [- 1]))) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 6 x + 4]}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 6

Diferencia con la regla de la cadena, que establece que $\frac{d}{d x} [f (g (x))]$ es $f' (g (x)) g' (x)$ donde $f (x) = e^{x}$ y $g (x) = x \ln (x)$ .

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Paso 6.1

Para aplicar la regla de la cadena, establece $u$ como $x \ln (x)$ .

$\frac{(x^{2} - 6 x + 4) (d (x^{2} - 3 x^{x} + 2 x - 1 + x (2 x - 3 (\frac{d}{d u} [e^{u}] \frac{d}{d x} [x \ln (x)]) + \frac{d}{d x} [2 x] + \frac{d}{d x} [- 1]))) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 6 x + 4]}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 6.2

Diferencia con la regla exponencial, que establece que $\frac{d}{d u} [a^{u}]$ es $a^{u} \ln (a)$ donde $a$ = $e$ .

$\frac{(x^{2} - 6 x + 4) (d (x^{2} - 3 x^{x} + 2 x - 1 + x (2 x - 3 (e^{u} \frac{d}{d x} [x \ln (x)]) + \frac{d}{d x} [2 x] + \frac{d}{d x} [- 1]))) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 6 x + 4]}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 6.3

Reemplaza todos los casos de $u$ con $x \ln (x)$ .

$\frac{(x^{2} - 6 x + 4) (d (x^{2} - 3 x^{x} + 2 x - 1 + x (2 x - 3 (e^{x \ln (x)} \frac{d}{d x} [x \ln (x)]) + \frac{d}{d x} [2 x] + \frac{d}{d x} [- 1]))) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 6 x + 4]}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 7

Diferencia con la regla del producto, que establece que $\frac{d}{d x} [f (x) g (x)]$ es $f (x) \frac{d}{d x} [g (x)] + g (x) \frac{d}{d x} [f (x)]$ donde $f (x) = x$ y $g (x) = \ln (x)$ .

$\frac{(x^{2} - 6 x + 4) (d (x^{2} - 3 x^{x} + 2 x - 1 + x (2 x - 3 e^{x \ln (x)} (x \frac{d}{d x} [\ln (x)] + \ln (x) \frac{d}{d x} [x]) + \frac{d}{d x} [2 x] + \frac{d}{d x} [- 1]))) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 6 x + 4]}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 8

La derivada de $\ln (x)$ con respecto a $x$ es $\frac{1}{x}$ .

$\frac{(x^{2} - 6 x + 4) (d (x^{2} - 3 x^{x} + 2 x - 1 + x (2 x - 3 e^{x \ln (x)} (x \frac{1}{x} + \ln (x) \frac{d}{d x} [x]) + \frac{d}{d x} [2 x] + \frac{d}{d x} [- 1]))) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 6 x + 4]}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 9

Diferencia.

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Paso 9.1

Combina $x$ y $\frac{1}{x}$ .

$\frac{(x^{2} - 6 x + 4) (d (x^{2} - 3 x^{x} + 2 x - 1 + x (2 x - 3 e^{x \ln (x)} (\frac{x}{x} + \ln (x) \frac{d}{d x} [x]) + \frac{d}{d x} [2 x] + \frac{d}{d x} [- 1]))) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 6 x + 4]}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 9.2

Cancela el factor común de $x$ .

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Paso 9.2.1

Cancela el factor común.

Paso 9.2.2

Reescribe la expresión.

$\frac{(x^{2} - 6 x + 4) (d (x^{2} - 3 x^{x} + 2 x - 1 + x (2 x - 3 e^{x \ln (x)} (1 + \ln (x) \frac{d}{d x} [x]) + \frac{d}{d x} [2 x] + \frac{d}{d x} [- 1]))) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 6 x + 4]}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 9.3

Diferencia con la regla de la potencia, que establece que $\frac{d}{d x} [x^{n}]$ es $n x^{n - 1}$ donde $n = 1$ .

$\frac{(x^{2} - 6 x + 4) (d (x^{2} - 3 x^{x} + 2 x - 1 + x (2 x - 3 e^{x \ln (x)} (1 + \ln (x) \cdot 1) + \frac{d}{d x} [2 x] + \frac{d}{d x} [- 1]))) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 6 x + 4]}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 9.4

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

$\frac{(x^{2} - 6 x + 4) (d (x^{2} - 3 x^{x} + 2 x - 1 + x (2 x - 3 e^{x \ln (x)} (1 + \ln (x)) + \frac{d}{d x} [2 x] + \frac{d}{d x} [- 1]))) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 6 x + 4]}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 9.5

Como $2$ es constante con respecto a $x$ , la derivada de $2 x$ con respecto a $x$ es $2 \frac{d}{d x} [x]$ .

$\frac{(x^{2} - 6 x + 4) (d (x^{2} - 3 x^{x} + 2 x - 1 + x (2 x - 3 e^{x \ln (x)} (1 + \ln (x)) + 2 \frac{d}{d x} [x] + \frac{d}{d x} [- 1]))) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 6 x + 4]}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 9.6

Diferencia con la regla de la potencia, que establece que $\frac{d}{d x} [x^{n}]$ es $n x^{n - 1}$ donde $n = 1$ .

$\frac{(x^{2} - 6 x + 4) (d (x^{2} - 3 x^{x} + 2 x - 1 + x (2 x - 3 e^{x \ln (x)} (1 + \ln (x)) + 2 \cdot 1 + \frac{d}{d x} [- 1]))) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 6 x + 4]}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 9.7

Multiplica $2$ por $1$ .

$\frac{(x^{2} - 6 x + 4) (d (x^{2} - 3 x^{x} + 2 x - 1 + x (2 x - 3 e^{x \ln (x)} (1 + \ln (x)) + 2 + \frac{d}{d x} [- 1]))) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 6 x + 4]}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 9.8

Como $- 1$ es constante con respecto a $x$ , la derivada de $- 1$ con respecto a $x$ es $0$ .

$\frac{(x^{2} - 6 x + 4) (d (x^{2} - 3 x^{x} + 2 x - 1 + x (2 x - 3 e^{x \ln (x)} (1 + \ln (x)) + 2 + 0))) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 6 x + 4]}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 9.9

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

$\frac{(x^{2} - 6 x + 4) (d (x^{2} - 3 x^{x} + 2 x - 1 + x (2 x - 3 e^{x \ln (x)} (1 + \ln (x)) + 2))) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 6 x + 4]}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 10

Simplifica.

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Paso 10.1

Aplica la propiedad distributiva.

$\frac{(x^{2} - 6 x + 4) (d (x^{2} - 3 x^{x} + 2 x - 1 + x (2 x - 3 e^{x \ln (x)} \cdot 1 - 3 e^{x \ln (x)} \ln (x) + 2))) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 6 x + 4]}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 10.2

Aplica la propiedad distributiva.

$\frac{(x^{2} - 6 x + 4) (d (x^{2} - 3 x^{x} + 2 x - 1 + x (2 x) + x (- 3 e^{x \ln (x)} \cdot 1) + x (- 3 e^{x \ln (x)} \ln (x)) + x \cdot 2)) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 6 x + 4]}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 10.3

Aplica la propiedad distributiva.

$\frac{(x^{2} - 6 x + 4) (d x^{2} + d (- 3 x^{x}) + d (2 x) + d \cdot - 1 + d (x (2 x)) + d (x (- 3 e^{x \ln (x)} \cdot 1)) + d (x (- 3 e^{x \ln (x)} \ln (x))) + d (x \cdot 2)) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 6 x + 4]}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 10.4

Combina los términos.

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Paso 10.4.1

Mueve $2$ a la izquierda de $d$ .

$\frac{(x^{2} - 6 x + 4) (d x^{2} + d (- 3 x^{x}) + 2 \cdot d x + d \cdot - 1 + d (x (2 x)) + d (x (- 3 e^{x \ln (x)} \cdot 1)) + d (x (- 3 e^{x \ln (x)} \ln (x))) + d (x \cdot 2)) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 6 x + 4]}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 10.4.2

Mueve $- 1$ a la izquierda de $d$ .

$\frac{(x^{2} - 6 x + 4) (d x^{2} + d (- 3 x^{x}) + 2 d x - 1 \cdot d + d (x (2 x)) + d (x (- 3 e^{x \ln (x)} \cdot 1)) + d (x (- 3 e^{x \ln (x)} \ln (x))) + d (x \cdot 2)) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 6 x + 4]}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 10.4.3

Reescribe $- 1 d$ como $- d$ .

$\frac{(x^{2} - 6 x + 4) (d x^{2} + d (- 3 x^{x}) + 2 d x - d + d (x (2 x)) + d (x (- 3 e^{x \ln (x)} \cdot 1)) + d (x (- 3 e^{x \ln (x)} \ln (x))) + d (x \cdot 2)) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 6 x + 4]}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 10.4.4

Eleva $x$ a la potencia de $1$ .

$\frac{(x^{2} - 6 x + 4) (d x^{2} + d (- 3 x^{x}) + 2 d x - d + d (2 (x^{1} x)) + d (x (- 3 e^{x \ln (x)} \cdot 1)) + d (x (- 3 e^{x \ln (x)} \ln (x))) + d (x \cdot 2)) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 6 x + 4]}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 10.4.5

Eleva $x$ a la potencia de $1$ .

$\frac{(x^{2} - 6 x + 4) (d x^{2} + d (- 3 x^{x}) + 2 d x - d + d (2 (x^{1} x^{1})) + d (x (- 3 e^{x \ln (x)} \cdot 1)) + d (x (- 3 e^{x \ln (x)} \ln (x))) + d (x \cdot 2)) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 6 x + 4]}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 10.4.6

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

$\frac{(x^{2} - 6 x + 4) (d x^{2} + d (- 3 x^{x}) + 2 d x - d + d (2 x^{1 + 1}) + d (x (- 3 e^{x \ln (x)} \cdot 1)) + d (x (- 3 e^{x \ln (x)} \ln (x))) + d (x \cdot 2)) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 6 x + 4]}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 10.4.7

Suma $1$ y $1$ .

$\frac{(x^{2} - 6 x + 4) (d x^{2} + d (- 3 x^{x}) + 2 d x - d + d (2 x^{2}) + d (x (- 3 e^{x \ln (x)} \cdot 1)) + d (x (- 3 e^{x \ln (x)} \ln (x))) + d (x \cdot 2)) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 6 x + 4]}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 10.4.8

Mueve $2$ a la izquierda de $d$ .

$\frac{(x^{2} - 6 x + 4) (d x^{2} + d (- 3 x^{x}) + 2 d x - d + 2 \cdot d x^{2} + d (x (- 3 e^{x \ln (x)} \cdot 1)) + d (x (- 3 e^{x \ln (x)} \ln (x))) + d (x \cdot 2)) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 6 x + 4]}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 10.4.9

Multiplica $- 3$ por $1$ .

$\frac{(x^{2} - 6 x + 4) (d x^{2} + d (- 3 x^{x}) + 2 d x - d + 2 d x^{2} + d (x (- 3 e^{x \ln (x)})) + d (x (- 3 e^{x \ln (x)} \ln (x))) + d (x \cdot 2)) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 6 x + 4]}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 10.4.10

Mueve $2$ a la izquierda de $x$ .

$\frac{(x^{2} - 6 x + 4) (d x^{2} + d (- 3 x^{x}) + 2 d x - d + 2 d x^{2} + d x (- 3 e^{x \ln (x)}) + d x (- 3 e^{x \ln (x)} \ln (x)) + d (2 \cdot x)) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 6 x + 4]}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 10.4.11

Mueve $2$ a la izquierda de $d$ .

$\frac{(x^{2} - 6 x + 4) (d x^{2} + d (- 3 x^{x}) + 2 d x - d + 2 d x^{2} + d x (- 3 e^{x \ln (x)}) + d x (- 3 e^{x \ln (x)} \ln (x)) + 2 \cdot d x) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 6 x + 4]}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 10.4.12

Suma $d x^{2}$ y $2 d x^{2}$ .

$\frac{(x^{2} - 6 x + 4) (d (- 3 x^{x}) + 2 d x - d + 3 d x^{2} + d x (- 3 e^{x \ln (x)}) + d x (- 3 e^{x \ln (x)} \ln (x)) + 2 d x) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 6 x + 4]}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 10.4.13

Suma $2 d x$ y $2 d x$ .

$\frac{(x^{2} - 6 x + 4) (d (- 3 x^{x}) - d + 3 d x^{2} + d x (- 3 e^{x \ln (x)}) + d x (- 3 e^{x \ln (x)} \ln (x)) + 4 d x) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 6 x + 4]}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 10.5

Reordena los términos.

$\frac{(x^{2} - 6 x + 4) (- d - 3 x^{x} d + 3 x^{2} d - 3 e^{x \ln (x)} d x - 3 e^{x \ln (x)} d x \ln (x) + 4 d x) - (x^{2} - 3 x^{x} + 2 x - 1) d x \frac{d}{d x} [x^{2} - 6 x + 4]}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 11

Diferencia.

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Paso 11.1

Según la regla de la suma, la derivada de $x^{2} - 6 x + 4$ con respecto a $x$ es $\frac{d}{d x} [x^{2}] + \frac{d}{d x} [- 6 x] + \frac{d}{d x} [4]$ .

$\frac{(x^{2} - 6 x + 4) (- d - 3 x^{x} d + 3 x^{2} d - 3 e^{x \ln (x)} d x - 3 e^{x \ln (x)} d x \ln (x) + 4 d x) - (x^{2} - 3 x^{x} + 2 x - 1) d x (\frac{d}{d x} [x^{2}] + \frac{d}{d x} [- 6 x] + \frac{d}{d x} [4])}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 11.2

Diferencia con la regla de la potencia, que establece que $\frac{d}{d x} [x^{n}]$ es $n x^{n - 1}$ donde $n = 2$ .

$\frac{(x^{2} - 6 x + 4) (- d - 3 x^{x} d + 3 x^{2} d - 3 e^{x \ln (x)} d x - 3 e^{x \ln (x)} d x \ln (x) + 4 d x) - (x^{2} - 3 x^{x} + 2 x - 1) d x (2 x + \frac{d}{d x} [- 6 x] + \frac{d}{d x} [4])}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 12

Evalúa $\frac{d}{d x} [- 6 x]$ .

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Paso 12.1

Como $- 6$ es constante con respecto a $x$ , la derivada de $- 6 x$ con respecto a $x$ es $- 6 \frac{d}{d x} [x]$ .

$\frac{(x^{2} - 6 x + 4) (- d - 3 x^{x} d + 3 x^{2} d - 3 e^{x \ln (x)} d x - 3 e^{x \ln (x)} d x \ln (x) + 4 d x) - (x^{2} - 3 x^{x} + 2 x - 1) d x (2 x - 6 \frac{d}{d x} [x] + \frac{d}{d x} [4])}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 12.2

Diferencia con la regla de la potencia, que establece que $\frac{d}{d x} [x^{n}]$ es $n x^{n - 1}$ donde $n = 1$ .

$\frac{(x^{2} - 6 x + 4) (- d - 3 x^{x} d + 3 x^{2} d - 3 e^{x \ln (x)} d x - 3 e^{x \ln (x)} d x \ln (x) + 4 d x) - (x^{2} - 3 x^{x} + 2 x - 1) d x (2 x - 6 \cdot 1 + \frac{d}{d x} [4])}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 12.3

Multiplica $- 6$ por $1$ .

$\frac{(x^{2} - 6 x + 4) (- d - 3 x^{x} d + 3 x^{2} d - 3 e^{x \ln (x)} d x - 3 e^{x \ln (x)} d x \ln (x) + 4 d x) - (x^{2} - 3 x^{x} + 2 x - 1) d x (2 x - 6 + \frac{d}{d x} [4])}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 13

Diferencia con la regla de la constante.

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Paso 13.1

Como $4$ es constante con respecto a $x$ , la derivada de $4$ con respecto a $x$ es $0$ .

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

Paso 13.2

Suma $2 x - 6$ y $0$ .

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

Paso 14

Simplifica.

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Paso 14.1

Aplica la propiedad distributiva.

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

Paso 14.2

Aplica la propiedad distributiva.

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

Paso 14.3

Aplica la propiedad distributiva.

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

Paso 14.4

Simplifica el numerador.

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Paso 14.4.1

Simplifica cada término.

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Paso 14.4.1.1

Simplifica cada término.

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Paso 14.4.1.1.1

Simplifica $- 3 \ln (x)$ al mover $3$ dentro del algoritmo.

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

Paso 14.4.1.1.2

Reescribe con la propiedad conmutativa de la multiplicación.

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

Paso 14.4.1.2

Expande $(x^{2} - 6 x + 4) (- d - 3 x^{x} d + 3 x^{2} d - 3 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{3}) + 4 d x)$ mediante la multiplicación de cada término de la primera expresión por cada término de la segunda expresión.

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

Paso 14.4.1.3

Simplifica cada término.

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Paso 14.4.1.3.1

Reescribe con la propiedad conmutativa de la multiplicación.

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

Paso 14.4.1.3.2

Reescribe con la propiedad conmutativa de la multiplicación.

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

Paso 14.4.1.3.3

Multiplica $x^{2}$ por $x^{x}$ sumando los exponentes.

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Paso 14.4.1.3.3.1

Mueve $x^{x}$ .

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

Paso 14.4.1.3.3.2

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

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

Paso 14.4.1.3.4

Reescribe con la propiedad conmutativa de la multiplicación.

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

Paso 14.4.1.3.5

Multiplica $x^{2}$ por $x^{2}$ sumando los exponentes.

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Paso 14.4.1.3.5.1

Mueve $x^{2}$ .

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

Paso 14.4.1.3.5.2

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

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

Paso 14.4.1.3.5.3

Suma $2$ y $2$ .

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

Paso 14.4.1.3.6

Reescribe con la propiedad conmutativa de la multiplicación.

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

Paso 14.4.1.3.7

Multiplica $x^{2}$ por $x$ sumando los exponentes.

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Paso 14.4.1.3.7.1

Mueve $x$ .

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

Paso 14.4.1.3.7.2

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

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Paso 14.4.1.3.7.2.1

Eleva $x$ a la potencia de $1$ .

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

Paso 14.4.1.3.7.2.2

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

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

Paso 14.4.1.3.7.3

Suma $1$ y $2$ .

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

Paso 14.4.1.3.8

Reescribe con la propiedad conmutativa de la multiplicación.

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

Paso 14.4.1.3.9

Multiplica $x^{2}$ por $x$ sumando los exponentes.

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Paso 14.4.1.3.9.1

Mueve $x$ .

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

Paso 14.4.1.3.9.2

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

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Paso 14.4.1.3.9.2.1

Eleva $x$ a la potencia de $1$ .

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

Paso 14.4.1.3.9.2.2

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

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

Paso 14.4.1.3.9.3

Suma $1$ y $2$ .

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

Paso 14.4.1.3.10

Reescribe con la propiedad conmutativa de la multiplicación.

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

Paso 14.4.1.3.11

Multiplica $x^{2}$ por $x$ sumando los exponentes.

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Paso 14.4.1.3.11.1

Mueve $x$ .

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

Paso 14.4.1.3.11.2

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

Toca para ver más pasos...

Paso 14.4.1.3.11.2.1

Eleva $x$ a la potencia de $1$ .

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

Paso 14.4.1.3.11.2.2

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

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

Paso 14.4.1.3.11.3

Suma $1$ y $2$ .

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

Paso 14.4.1.3.12

Reescribe con la propiedad conmutativa de la multiplicación.

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

Paso 14.4.1.3.13

Multiplica $- 6$ por $- 1$ .

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

Paso 14.4.1.3.14

Multiplica $x$ por $x^{x}$ sumando los exponentes.

Toca para ver más pasos...

Paso 14.4.1.3.14.1

Mueve $x^{x}$ .

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

Paso 14.4.1.3.14.2

Multiplica $x^{x}$ por $x$ .

Toca para ver más pasos...

Paso 14.4.1.3.14.2.1

Eleva $x$ a la potencia de $1$ .

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

Paso 14.4.1.3.14.2.2

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

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

Paso 14.4.1.3.15

Reescribe con la propiedad conmutativa de la multiplicación.

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

Paso 14.4.1.3.16

Multiplica $- 6$ por $- 3$ .

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

Paso 14.4.1.3.17

Multiplica $x$ por $x^{2}$ sumando los exponentes.

Toca para ver más pasos...

Paso 14.4.1.3.17.1

Mueve $x^{2}$ .

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

Paso 14.4.1.3.17.2

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

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Paso 14.4.1.3.17.2.1

Eleva $x$ a la potencia de $1$ .

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

Paso 14.4.1.3.17.2.2

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

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

Paso 14.4.1.3.17.3

Suma $2$ y $1$ .

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

Paso 14.4.1.3.18

Reescribe con la propiedad conmutativa de la multiplicación.

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

Paso 14.4.1.3.19

Multiplica $- 6$ por $3$ .

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

Paso 14.4.1.3.20

Multiplica $x$ por $x$ sumando los exponentes.

Toca para ver más pasos...

Paso 14.4.1.3.20.1

Mueve $x$ .

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

Paso 14.4.1.3.20.2

Multiplica $x$ por $x$ .

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

Paso 14.4.1.3.21

Multiplica $- 3$ por $- 6$ .

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

Paso 14.4.1.3.22

Multiplica $x$ por $x$ sumando los exponentes.

Toca para ver más pasos...

Paso 14.4.1.3.22.1

Mueve $x$ .

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

Paso 14.4.1.3.22.2

Multiplica $x$ por $x$ .

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

Paso 14.4.1.3.23

Multiplica $- 6 x^{2} (- e^{x \ln (x)} d \ln (x^{3}))$ .

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Paso 14.4.1.3.23.1

Multiplica $- 1$ por $- 6$ .

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

Paso 14.4.1.3.23.2

Simplifica $6 \ln (x^{3})$ al mover $6$ dentro del algoritmo.

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

Paso 14.4.1.3.24

Multiplica los exponentes en ${(x^{3})}^{6}$ .

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Paso 14.4.1.3.24.1

Aplica la regla de la potencia y multiplica los exponentes, ${(a^{m})}^{n} = a^{m n}$ .

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

Paso 14.4.1.3.24.2

Multiplica $3$ por $6$ .

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

Paso 14.4.1.3.25

Multiplica $x$ por $x$ sumando los exponentes.

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Paso 14.4.1.3.25.1

Mueve $x$ .

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

Paso 14.4.1.3.25.2

Multiplica $x$ por $x$ .

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

Paso 14.4.1.3.26

Reescribe con la propiedad conmutativa de la multiplicación.

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

Paso 14.4.1.3.27

Multiplica $- 6$ por $4$ .

$\frac{- x^{2} d - 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) + 4 x^{3} d + 6 x d + 18 x^{x + 1} d - 18 x^{3} d + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 24 x^{2} d + 4 (- d) + 4 (- 3 x^{x} d) + 4 (3 x^{2} d) + 4 (- 3 e^{x \ln (x)} d x) + 4 (- e^{x \ln (x)} d x \ln (x^{3})) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 6)}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 14.4.1.3.28

Multiplica $- 1$ por $4$ .

$\frac{- x^{2} d - 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) + 4 x^{3} d + 6 x d + 18 x^{x + 1} d - 18 x^{3} d + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 24 x^{2} d - 4 d + 4 (- 3 x^{x} d) + 4 (3 x^{2} d) + 4 (- 3 e^{x \ln (x)} d x) + 4 (- e^{x \ln (x)} d x \ln (x^{3})) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 6)}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 14.4.1.3.29

Multiplica $- 3$ por $4$ .

$\frac{- x^{2} d - 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) + 4 x^{3} d + 6 x d + 18 x^{x + 1} d - 18 x^{3} d + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 24 x^{2} d - 4 d - 12 (x^{x} d) + 4 (3 x^{2} d) + 4 (- 3 e^{x \ln (x)} d x) + 4 (- e^{x \ln (x)} d x \ln (x^{3})) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 6)}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 14.4.1.3.30

Multiplica $3$ por $4$ .

$\frac{- x^{2} d - 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) + 4 x^{3} d + 6 x d + 18 x^{x + 1} d - 18 x^{3} d + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 24 x^{2} d - 4 d - 12 x^{x} d + 12 (x^{2} d) + 4 (- 3 e^{x \ln (x)} d x) + 4 (- e^{x \ln (x)} d x \ln (x^{3})) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 6)}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 14.4.1.3.31

Multiplica $- 3$ por $4$ .

$\frac{- x^{2} d - 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) + 4 x^{3} d + 6 x d + 18 x^{x + 1} d - 18 x^{3} d + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 24 x^{2} d - 4 d - 12 x^{x} d + 12 x^{2} d - 12 (e^{x \ln (x)} d x) + 4 (- e^{x \ln (x)} d x \ln (x^{3})) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 6)}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 14.4.1.3.32

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

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Paso 14.4.1.3.32.1

Multiplica $- 1$ por $4$ .

$\frac{- x^{2} d - 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) + 4 x^{3} d + 6 x d + 18 x^{x + 1} d - 18 x^{3} d + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 24 x^{2} d - 4 d - 12 x^{x} d + 12 x^{2} d - 12 e^{x \ln (x)} d x - 4 (e^{x \ln (x)} d x \ln (x^{3})) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 6)}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 14.4.1.3.32.2

Simplifica $- 4 \ln (x^{3})$ al mover $4$ dentro del algoritmo.

$\frac{- x^{2} d - 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) + 4 x^{3} d + 6 x d + 18 x^{x + 1} d - 18 x^{3} d + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 24 x^{2} d - 4 d - 12 x^{x} d + 12 x^{2} d - 12 e^{x \ln (x)} d x + e^{x \ln (x)} d x (- \ln ({(x^{3})}^{4})) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 6)}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 14.4.1.3.33

Reescribe con la propiedad conmutativa de la multiplicación.

$\frac{- x^{2} d - 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) + 4 x^{3} d + 6 x d + 18 x^{x + 1} d - 18 x^{3} d + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 24 x^{2} d - 4 d - 12 x^{x} d + 12 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln ({(x^{3})}^{4}) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 6)}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 14.4.1.3.34

Multiplica los exponentes en ${(x^{3})}^{4}$ .

Toca para ver más pasos...

Paso 14.4.1.3.34.1

Aplica la regla de la potencia y multiplica los exponentes, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{- x^{2} d - 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) + 4 x^{3} d + 6 x d + 18 x^{x + 1} d - 18 x^{3} d + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 24 x^{2} d - 4 d - 12 x^{x} d + 12 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{3 \cdot 4}) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 6)}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 14.4.1.3.34.2

Multiplica $3$ por $4$ .

$\frac{- x^{2} d - 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) + 4 x^{3} d + 6 x d + 18 x^{x + 1} d - 18 x^{3} d + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 24 x^{2} d - 4 d - 12 x^{x} d + 12 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 4 (4 d x) + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 6)}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 14.4.1.3.35

Multiplica $4$ por $4$ .

$\frac{- x^{2} d - 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) + 4 x^{3} d + 6 x d + 18 x^{x + 1} d - 18 x^{3} d + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 24 x^{2} d - 4 d - 12 x^{x} d + 12 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 16 d x + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 6)}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 14.4.1.4

Resta $24 x^{2} d$ de $- x^{2} d$ .

$\frac{- 25 x^{2} d - 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) + 4 x^{3} d + 6 x d + 18 x^{x + 1} d - 18 x^{3} d + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 4 d - 12 x^{x} d + 12 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 16 d x + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 6)}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 14.4.1.5

Suma $- 25 x^{2} d$ y $12 x^{2} d$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) + 4 x^{3} d + 6 x d + 18 x^{x + 1} d - 18 x^{3} d + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 4 d - 12 x^{x} d - 13 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 16 d x + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 6)}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 14.4.1.6

Resta $18 x^{3} d$ de $4 x^{3} d$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 14 x^{3} d + 6 x d + 18 x^{x + 1} d + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 4 d - 12 x^{x} d - 13 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 16 d x + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 6)}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 14.4.1.7

Suma $6 x d$ y $16 d x$ .

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Paso 14.4.1.7.1

Mueve $x$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 14 x^{3} d + 18 x^{x + 1} d + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 4 d - 12 x^{x} d - 13 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 6 d x + 16 d x + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 6)}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 14.4.1.7.2

Suma $6 d x$ y $16 d x$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 14 x^{3} d + 18 x^{x + 1} d + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 4 d - 12 x^{x} d - 13 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 22 d x + (- x^{2} d x - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 6)}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 14.4.1.8

Simplifica cada término.

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Paso 14.4.1.8.1

Multiplica $x^{2}$ por $x$ sumando los exponentes.

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Paso 14.4.1.8.1.1

Mueve $x$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 14 x^{3} d + 18 x^{x + 1} d + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 4 d - 12 x^{x} d - 13 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 22 d x + (- (x \cdot x^{2}) d - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 6)}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 14.4.1.8.1.2

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

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Paso 14.4.1.8.1.2.1

Eleva $x$ a la potencia de $1$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 14 x^{3} d + 18 x^{x + 1} d + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 4 d - 12 x^{x} d - 13 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 22 d x + (- (x^{1} x^{2}) d - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 6)}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 14.4.1.8.1.2.2

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 14 x^{3} d + 18 x^{x + 1} d + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 4 d - 12 x^{x} d - 13 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 22 d x + (- x^{1 + 2} d - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 6)}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 14.4.1.8.1.3

Suma $1$ y $2$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 14 x^{3} d + 18 x^{x + 1} d + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 4 d - 12 x^{x} d - 13 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 22 d x + (- x^{3} d - (- 3 x^{x}) d x - (2 x) d x - - 1 d x) (2 x - 6)}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 14.4.1.8.2

Multiplica $x^{x}$ por $x$ sumando los exponentes.

Toca para ver más pasos...

Paso 14.4.1.8.2.1

Mueve $x$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 14 x^{3} d + 18 x^{x + 1} d + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 4 d - 12 x^{x} d - 13 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 22 d x + (- x^{3} d - (- 3 (x \cdot x^{x})) d - (2 x) d x - - 1 d x) (2 x - 6)}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 14.4.1.8.2.2

Multiplica $x$ por $x^{x}$ .

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Paso 14.4.1.8.2.2.1

Eleva $x$ a la potencia de $1$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 14 x^{3} d + 18 x^{x + 1} d + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 4 d - 12 x^{x} d - 13 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 22 d x + (- x^{3} d - (- 3 (x^{1} x^{x})) d - (2 x) d x - - 1 d x) (2 x - 6)}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 14.4.1.8.2.2.2

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 14 x^{3} d + 18 x^{x + 1} d + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 4 d - 12 x^{x} d - 13 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 22 d x + (- x^{3} d - (- 3 x^{1 + x}) d - (2 x) d x - - 1 d x) (2 x - 6)}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 14.4.1.8.3

Multiplica $- 3$ por $- 1$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 14 x^{3} d + 18 x^{x + 1} d + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 4 d - 12 x^{x} d - 13 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 22 d x + (- x^{3} d + 3 x^{1 + x} d - (2 x) d x - - 1 d x) (2 x - 6)}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 14.4.1.8.4

Multiplica $x$ por $x$ sumando los exponentes.

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Paso 14.4.1.8.4.1

Mueve $x$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 14 x^{3} d + 18 x^{x + 1} d + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 4 d - 12 x^{x} d - 13 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 22 d x + (- x^{3} d + 3 x^{1 + x} d - (2 (x \cdot x)) d - - 1 d x) (2 x - 6)}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 14.4.1.8.4.2

Multiplica $x$ por $x$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 14 x^{3} d + 18 x^{x + 1} d + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 4 d - 12 x^{x} d - 13 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 22 d x + (- x^{3} d + 3 x^{1 + x} d - (2 x^{2}) d - - 1 d x) (2 x - 6)}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 14.4.1.8.5

Multiplica $2$ por $- 1$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 14 x^{3} d + 18 x^{x + 1} d + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 4 d - 12 x^{x} d - 13 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 22 d x + (- x^{3} d + 3 x^{1 + x} d - 2 x^{2} d - - 1 d x) (2 x - 6)}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 14.4.1.8.6

Multiplica $- 1$ por $- 1$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 14 x^{3} d + 18 x^{x + 1} d + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 4 d - 12 x^{x} d - 13 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 22 d x + (- x^{3} d + 3 x^{1 + x} d - 2 x^{2} d + 1 d x) (2 x - 6)}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 14.4.1.8.7

Multiplica $d$ por $1$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 14 x^{3} d + 18 x^{x + 1} d + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 4 d - 12 x^{x} d - 13 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 22 d x + (- x^{3} d + 3 x^{1 + x} d - 2 x^{2} d + d x) (2 x - 6)}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 14.4.1.9

Expande $(- x^{3} d + 3 x^{1 + x} d - 2 x^{2} d + d x) (2 x - 6)$ mediante la multiplicación de cada término de la primera expresión por cada término de la segunda expresión.

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 14 x^{3} d + 18 x^{x + 1} d + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 4 d - 12 x^{x} d - 13 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 22 d x - x^{3} d (2 x) - x^{3} d \cdot - 6 + 3 x^{1 + x} d (2 x) + 3 x^{1 + x} d \cdot - 6 - 2 x^{2} d (2 x) - 2 x^{2} d \cdot - 6 + d x (2 x) + d x \cdot - 6}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 14.4.1.10

Simplifica cada término.

Toca para ver más pasos...

Paso 14.4.1.10.1

Multiplica $x^{3}$ por $x$ sumando los exponentes.

Toca para ver más pasos...

Paso 14.4.1.10.1.1

Mueve $x$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 14 x^{3} d + 18 x^{x + 1} d + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 4 d - 12 x^{x} d - 13 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 22 d x - (x \cdot x^{3}) d \cdot 2 - x^{3} d \cdot - 6 + 3 x^{1 + x} d (2 x) + 3 x^{1 + x} d \cdot - 6 - 2 x^{2} d (2 x) - 2 x^{2} d \cdot - 6 + d x (2 x) + d x \cdot - 6}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 14.4.1.10.1.2

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

Toca para ver más pasos...

Paso 14.4.1.10.1.2.1

Eleva $x$ a la potencia de $1$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 14 x^{3} d + 18 x^{x + 1} d + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 4 d - 12 x^{x} d - 13 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 22 d x - (x^{1} x^{3}) d \cdot 2 - x^{3} d \cdot - 6 + 3 x^{1 + x} d (2 x) + 3 x^{1 + x} d \cdot - 6 - 2 x^{2} d (2 x) - 2 x^{2} d \cdot - 6 + d x (2 x) + d x \cdot - 6}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 14.4.1.10.1.2.2

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 14 x^{3} d + 18 x^{x + 1} d + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 4 d - 12 x^{x} d - 13 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 22 d x - x^{1 + 3} d \cdot 2 - x^{3} d \cdot - 6 + 3 x^{1 + x} d (2 x) + 3 x^{1 + x} d \cdot - 6 - 2 x^{2} d (2 x) - 2 x^{2} d \cdot - 6 + d x (2 x) + d x \cdot - 6}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 14.4.1.10.1.3

Suma $1$ y $3$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 14 x^{3} d + 18 x^{x + 1} d + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 4 d - 12 x^{x} d - 13 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 22 d x - x^{4} d \cdot 2 - x^{3} d \cdot - 6 + 3 x^{1 + x} d (2 x) + 3 x^{1 + x} d \cdot - 6 - 2 x^{2} d (2 x) - 2 x^{2} d \cdot - 6 + d x (2 x) + d x \cdot - 6}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 14.4.1.10.2

Multiplica $2$ por $- 1$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 14 x^{3} d + 18 x^{x + 1} d + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 4 d - 12 x^{x} d - 13 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 22 d x - 2 x^{4} d - x^{3} d \cdot - 6 + 3 x^{1 + x} d (2 x) + 3 x^{1 + x} d \cdot - 6 - 2 x^{2} d (2 x) - 2 x^{2} d \cdot - 6 + d x (2 x) + d x \cdot - 6}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 14.4.1.10.3

Multiplica $- 6$ por $- 1$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 14 x^{3} d + 18 x^{x + 1} d + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 4 d - 12 x^{x} d - 13 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 22 d x - 2 x^{4} d + 6 x^{3} d + 3 x^{1 + x} d (2 x) + 3 x^{1 + x} d \cdot - 6 - 2 x^{2} d (2 x) - 2 x^{2} d \cdot - 6 + d x (2 x) + d x \cdot - 6}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 14.4.1.10.4

Multiplica $x^{1 + x}$ por $x$ sumando los exponentes.

Toca para ver más pasos...

Paso 14.4.1.10.4.1

Mueve $x$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 14 x^{3} d + 18 x^{x + 1} d + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 4 d - 12 x^{x} d - 13 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 22 d x - 2 x^{4} d + 6 x^{3} d + 3 (x \cdot x^{1 + x}) d \cdot 2 + 3 x^{1 + x} d \cdot - 6 - 2 x^{2} d (2 x) - 2 x^{2} d \cdot - 6 + d x (2 x) + d x \cdot - 6}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 14.4.1.10.4.2

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

Toca para ver más pasos...

Paso 14.4.1.10.4.2.1

Eleva $x$ a la potencia de $1$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 14 x^{3} d + 18 x^{x + 1} d + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 4 d - 12 x^{x} d - 13 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 22 d x - 2 x^{4} d + 6 x^{3} d + 3 (x^{1} x^{1 + x}) d \cdot 2 + 3 x^{1 + x} d \cdot - 6 - 2 x^{2} d (2 x) - 2 x^{2} d \cdot - 6 + d x (2 x) + d x \cdot - 6}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 14.4.1.10.4.2.2

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 14 x^{3} d + 18 x^{x + 1} d + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 4 d - 12 x^{x} d - 13 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 22 d x - 2 x^{4} d + 6 x^{3} d + 3 x^{1 + 1 + x} d \cdot 2 + 3 x^{1 + x} d \cdot - 6 - 2 x^{2} d (2 x) - 2 x^{2} d \cdot - 6 + d x (2 x) + d x \cdot - 6}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 14.4.1.10.4.3

Suma $1$ y $1$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 14 x^{3} d + 18 x^{x + 1} d + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 4 d - 12 x^{x} d - 13 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 22 d x - 2 x^{4} d + 6 x^{3} d + 3 x^{2 + x} d \cdot 2 + 3 x^{1 + x} d \cdot - 6 - 2 x^{2} d (2 x) - 2 x^{2} d \cdot - 6 + d x (2 x) + d x \cdot - 6}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 14.4.1.10.5

Multiplica $2$ por $3$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 14 x^{3} d + 18 x^{x + 1} d + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 4 d - 12 x^{x} d - 13 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 22 d x - 2 x^{4} d + 6 x^{3} d + 6 x^{2 + x} d + 3 x^{1 + x} d \cdot - 6 - 2 x^{2} d (2 x) - 2 x^{2} d \cdot - 6 + d x (2 x) + d x \cdot - 6}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 14.4.1.10.6

Multiplica $- 6$ por $3$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 14 x^{3} d + 18 x^{x + 1} d + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 4 d - 12 x^{x} d - 13 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 22 d x - 2 x^{4} d + 6 x^{3} d + 6 x^{2 + x} d - 18 x^{1 + x} d - 2 x^{2} d (2 x) - 2 x^{2} d \cdot - 6 + d x (2 x) + d x \cdot - 6}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 14.4.1.10.7

Multiplica $x^{2}$ por $x$ sumando los exponentes.

Toca para ver más pasos...

Paso 14.4.1.10.7.1

Mueve $x$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 14 x^{3} d + 18 x^{x + 1} d + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 4 d - 12 x^{x} d - 13 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 22 d x - 2 x^{4} d + 6 x^{3} d + 6 x^{2 + x} d - 18 x^{1 + x} d - 2 (x \cdot x^{2}) d \cdot 2 - 2 x^{2} d \cdot - 6 + d x (2 x) + d x \cdot - 6}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 14.4.1.10.7.2

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

Toca para ver más pasos...

Paso 14.4.1.10.7.2.1

Eleva $x$ a la potencia de $1$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 14 x^{3} d + 18 x^{x + 1} d + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 4 d - 12 x^{x} d - 13 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 22 d x - 2 x^{4} d + 6 x^{3} d + 6 x^{2 + x} d - 18 x^{1 + x} d - 2 (x^{1} x^{2}) d \cdot 2 - 2 x^{2} d \cdot - 6 + d x (2 x) + d x \cdot - 6}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 14.4.1.10.7.2.2

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 14 x^{3} d + 18 x^{x + 1} d + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 4 d - 12 x^{x} d - 13 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 22 d x - 2 x^{4} d + 6 x^{3} d + 6 x^{2 + x} d - 18 x^{1 + x} d - 2 x^{1 + 2} d \cdot 2 - 2 x^{2} d \cdot - 6 + d x (2 x) + d x \cdot - 6}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 14.4.1.10.7.3

Suma $1$ y $2$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 14 x^{3} d + 18 x^{x + 1} d + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 4 d - 12 x^{x} d - 13 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 22 d x - 2 x^{4} d + 6 x^{3} d + 6 x^{2 + x} d - 18 x^{1 + x} d - 2 x^{3} d \cdot 2 - 2 x^{2} d \cdot - 6 + d x (2 x) + d x \cdot - 6}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 14.4.1.10.8

Multiplica $2$ por $- 2$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 14 x^{3} d + 18 x^{x + 1} d + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 4 d - 12 x^{x} d - 13 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 22 d x - 2 x^{4} d + 6 x^{3} d + 6 x^{2 + x} d - 18 x^{1 + x} d - 4 x^{3} d - 2 x^{2} d \cdot - 6 + d x (2 x) + d x \cdot - 6}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 14.4.1.10.9

Multiplica $- 6$ por $- 2$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 14 x^{3} d + 18 x^{x + 1} d + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 4 d - 12 x^{x} d - 13 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 22 d x - 2 x^{4} d + 6 x^{3} d + 6 x^{2 + x} d - 18 x^{1 + x} d - 4 x^{3} d + 12 x^{2} d + d x (2 x) + d x \cdot - 6}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 14.4.1.10.10

Reescribe con la propiedad conmutativa de la multiplicación.

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 14 x^{3} d + 18 x^{x + 1} d + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 4 d - 12 x^{x} d - 13 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 22 d x - 2 x^{4} d + 6 x^{3} d + 6 x^{2 + x} d - 18 x^{1 + x} d - 4 x^{3} d + 12 x^{2} d + 2 d x \cdot x + d x \cdot - 6}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 14.4.1.10.11

Multiplica $x$ por $x$ sumando los exponentes.

Toca para ver más pasos...

Paso 14.4.1.10.11.1

Mueve $x$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 14 x^{3} d + 18 x^{x + 1} d + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 4 d - 12 x^{x} d - 13 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 22 d x - 2 x^{4} d + 6 x^{3} d + 6 x^{2 + x} d - 18 x^{1 + x} d - 4 x^{3} d + 12 x^{2} d + 2 d (x \cdot x) + d x \cdot - 6}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 14.4.1.10.11.2

Multiplica $x$ por $x$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 14 x^{3} d + 18 x^{x + 1} d + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 4 d - 12 x^{x} d - 13 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 22 d x - 2 x^{4} d + 6 x^{3} d + 6 x^{2 + x} d - 18 x^{1 + x} d - 4 x^{3} d + 12 x^{2} d + 2 d x^{2} + d x \cdot - 6}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 14.4.1.10.12

Mueve $- 6$ a la izquierda de $d x$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 14 x^{3} d + 18 x^{x + 1} d + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 4 d - 12 x^{x} d - 13 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 22 d x - 2 x^{4} d + 6 x^{3} d + 6 x^{2 + x} d - 18 x^{1 + x} d - 4 x^{3} d + 12 x^{2} d + 2 d x^{2} - 6 d x}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 14.4.1.11

Resta $4 x^{3} d$ de $6 x^{3} d$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 14 x^{3} d + 18 x^{x + 1} d + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 4 d - 12 x^{x} d - 13 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 22 d x - 2 x^{4} d + 2 x^{3} d + 6 x^{2 + x} d - 18 x^{1 + x} d + 12 x^{2} d + 2 d x^{2} - 6 d x}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 14.4.1.12

Suma $12 x^{2} d$ y $2 d x^{2}$ .

Toca para ver más pasos...

Paso 14.4.1.12.1

Mueve $x^{2}$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 14 x^{3} d + 18 x^{x + 1} d + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 4 d - 12 x^{x} d - 13 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 22 d x - 2 x^{4} d + 2 x^{3} d + 6 x^{2 + x} d - 18 x^{1 + x} d + 12 d x^{2} + 2 d x^{2} - 6 d x}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 14.4.1.12.2

Suma $12 d x^{2}$ y $2 d x^{2}$ .

$\frac{- 3 x^{x + 2} d + 3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 14 x^{3} d + 18 x^{x + 1} d + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 4 d - 12 x^{x} d - 13 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 22 d x - 2 x^{4} d + 2 x^{3} d + 6 x^{2 + x} d - 18 x^{1 + x} d + 14 d x^{2} - 6 d x}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 14.4.2

Mueve $x^{x + 2}$ .

$\frac{3 x^{4} d - 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 14 x^{3} d + 18 x^{x + 1} d + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 4 d - 12 x^{x} d - 13 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 22 d x - 2 x^{4} d + 2 x^{3} d - 3 d x^{x + 2} + 6 d x^{x + 2} - 18 x^{1 + x} d + 14 d x^{2} - 6 d x}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 14.4.3

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

$\frac{- 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 14 x^{3} d + 18 x^{x + 1} d + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 4 d - 12 x^{x} d - 13 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 22 d x + 1 x^{4} d + 2 x^{3} d - 3 d x^{x + 2} + 6 d x^{x + 2} - 18 x^{1 + x} d + 14 d x^{2} - 6 d x}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 14.4.4

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

$\frac{- 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) - 14 x^{3} d + 18 x^{x + 1} d + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 4 d - 12 x^{x} d - 13 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 22 d x + x^{4} d + 2 x^{3} d - 3 d x^{x + 2} + 6 d x^{x + 2} - 18 x^{1 + x} d + 14 d x^{2} - 6 d x}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 14.4.5

Suma $- 14 x^{3} d$ y $2 x^{3} d$ .

$\frac{- 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) + 18 x^{x + 1} d + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 4 d - 12 x^{x} d - 13 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 22 d x + x^{4} d - 12 x^{3} d - 3 d x^{x + 2} + 6 d x^{x + 2} - 18 x^{1 + x} d + 14 d x^{2} - 6 d x}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 14.4.6

Mueve $x^{x + 1}$ .

$\frac{- 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 4 d - 12 x^{x} d - 13 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 22 d x + x^{4} d - 12 x^{3} d - 3 d x^{x + 2} + 6 d x^{x + 2} + 18 d x^{x + 1} - 18 d x^{x + 1} + 14 d x^{2} - 6 d x}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 14.4.7

Combina los términos opuestos en $- 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 4 d - 12 x^{x} d - 13 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 22 d x + x^{4} d - 12 x^{3} d - 3 d x^{x + 2} + 6 d x^{x + 2} + 18 d x^{x + 1} - 18 d x^{x + 1} + 14 d x^{2} - 6 d x$ .

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Paso 14.4.7.1

Resta $18 d x^{x + 1}$ de $18 d x^{x + 1}$ .

Paso 14.4.7.2

Suma $- 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 4 d - 12 x^{x} d - 13 x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 22 d x + x^{4} d - 12 x^{3} d - 3 d x^{x + 2} + 6 d x^{x + 2}$ y $0$ .

Paso 14.4.8

Suma $- 13 x^{2} d$ y $14 d x^{2}$ .

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Paso 14.4.8.1

Mueve $x^{2}$ .

$\frac{- 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 4 d - 12 x^{x} d - 13 d x^{2} + 14 d x^{2} - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 22 d x + x^{4} d - 12 x^{3} d - 3 d x^{x + 2} + 6 d x^{x + 2} - 6 d x}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 14.4.8.2

Suma $- 13 d x^{2}$ y $14 d x^{2}$ .

$\frac{- 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 4 d - 12 x^{x} d + 1 d x^{2} - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 22 d x + x^{4} d - 12 x^{3} d - 3 d x^{x + 2} + 6 d x^{x + 2} - 6 d x}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 14.4.9

Multiplica $d$ por $1$ .

$\frac{- 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 4 d - 12 x^{x} d + d x^{2} - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 22 d x + x^{4} d - 12 x^{3} d - 3 d x^{x + 2} + 6 d x^{x + 2} - 6 d x}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 14.4.10

Resta $6 d x$ de $22 d x$ .

$\frac{- 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 4 d - 12 x^{x} d + d x^{2} - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 16 d x + x^{4} d - 12 x^{3} d - 3 d x^{x + 2} + 6 d x^{x + 2}}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 14.4.11

Suma $- 3 d x^{x + 2}$ y $6 d x^{x + 2}$ .

$\frac{- 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 4 d - 12 x^{x} d + d x^{2} - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 16 d x + x^{4} d - 12 x^{3} d + 3 d x^{x + 2}}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 14.4.12

Reordena los factores en $- 3 x^{3} (e^{x \ln (x)} d) - x^{3} (e^{x \ln (x)} d \ln (x^{3})) + 18 x^{2} (e^{x \ln (x)} d) + x^{2} (e^{x \ln (x)} d \ln (x^{18})) - 4 d - 12 x^{x} d + d x^{2} - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 16 d x + x^{4} d - 12 x^{3} d + 3 d x^{x + 2}$ .

$\frac{- 3 x^{3} d e^{x \ln (x)} - x^{3} d e^{x \ln (x)} \ln (x^{3}) + 18 x^{2} d e^{x \ln (x)} + x^{2} d e^{x \ln (x)} \ln (x^{18}) - 4 d - 12 d x^{x} + d x^{2} - 12 d x e^{x \ln (x)} - d x e^{x \ln (x)} \ln (x^{12}) + 16 d x + x^{4} d - 12 x^{3} d + 3 d x^{x + 2}}{{(x^{2} - 6 x + 4)}^{2}}$

Paso 14.5

Reordena los términos.

$\frac{- 4 d - 3 e^{x \ln (x)} x^{3} d - e^{x \ln (x)} x^{3} d \ln (x^{3}) + 18 e^{x \ln (x)} x^{2} d + e^{x \ln (x)} x^{2} d \ln (x^{18}) - 12 x^{x} d + x^{2} d - 12 e^{x \ln (x)} d x - e^{x \ln (x)} d x \ln (x^{12}) + 16 d x + x^{4} d - 12 x^{3} d + 3 x^{x + 2} d}{{(x^{2} - 6 x + 4)}^{2}}$