Cálculo Ejemplos

$y = \ln (\sec (2 x) + \tan (2 x))$

Paso 1

Obtén la primera derivada.

Toca para ver más pasos...

Paso 1.1

Diferencia con la regla de la cadena, que establece que $\frac{d}{d x} [f (g (x))]$ es $f' (g (x)) g' (x)$ donde $f (x) = \ln (x)$ y $g (x) = \sec (2 x) + \tan (2 x)$ .

Toca para ver más pasos...

Paso 1.1.1

Para aplicar la regla de la cadena, establece $u_{1}$ como $\sec (2 x) + \tan (2 x)$ .

$\frac{d}{d u_{1}} [\ln (u_{1})] \frac{d}{d x} [\sec (2 x) + \tan (2 x)]$

Paso 1.1.2

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

$\frac{1}{u_{1}} \frac{d}{d x} [\sec (2 x) + \tan (2 x)]$

Paso 1.1.3

Reemplaza todos los casos de $u_{1}$ con $\sec (2 x) + \tan (2 x)$ .

$\frac{1}{\sec (2 x) + \tan (2 x)} \frac{d}{d x} [\sec (2 x) + \tan (2 x)]$

Paso 1.2

Según la regla de la suma, la derivada de $\sec (2 x) + \tan (2 x)$ con respecto a $x$ es $\frac{d}{d x} [\sec (2 x)] + \frac{d}{d x} [\tan (2 x)]$ .

$\frac{1}{\sec (2 x) + \tan (2 x)} (\frac{d}{d x} [\sec (2 x)] + \frac{d}{d x} [\tan (2 x)])$

Paso 1.3

Diferencia con la regla de la cadena, que establece que $\frac{d}{d x} [f (g (x))]$ es $f' (g (x)) g' (x)$ donde $f (x) = \sec (x)$ y $g (x) = 2 x$ .

Toca para ver más pasos...

Paso 1.3.1

Para aplicar la regla de la cadena, establece $u_{2}$ como $2 x$ .

$\frac{1}{\sec (2 x) + \tan (2 x)} (\frac{d}{d u_{2}} [\sec (u_{2})] \frac{d}{d x} [2 x] + \frac{d}{d x} [\tan (2 x)])$

Paso 1.3.2

La derivada de $\sec (u_{2})$ con respecto a $u_{2}$ es $\sec (u_{2}) \tan (u_{2})$ .

$\frac{1}{\sec (2 x) + \tan (2 x)} (\sec (u_{2}) \tan (u_{2}) \frac{d}{d x} [2 x] + \frac{d}{d x} [\tan (2 x)])$

Paso 1.3.3

Reemplaza todos los casos de $u_{2}$ con $2 x$ .

$\frac{1}{\sec (2 x) + \tan (2 x)} (\sec (2 x) \tan (2 x) \frac{d}{d x} [2 x] + \frac{d}{d x} [\tan (2 x)])$

Paso 1.4

Diferencia.

Toca para ver más pasos...

Paso 1.4.1

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

$\frac{1}{\sec (2 x) + \tan (2 x)} (\sec (2 x) \tan (2 x) (2 \frac{d}{d x} [x]) + \frac{d}{d x} [\tan (2 x)])$

Paso 1.4.2

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

$\frac{1}{\sec (2 x) + \tan (2 x)} (\sec (2 x) \tan (2 x) (2 \cdot 1) + \frac{d}{d x} [\tan (2 x)])$

Paso 1.4.3

Simplifica la expresión.

Toca para ver más pasos...

Paso 1.4.3.1

Multiplica $2$ por $1$ .

$\frac{1}{\sec (2 x) + \tan (2 x)} (\sec (2 x) \tan (2 x) \cdot 2 + \frac{d}{d x} [\tan (2 x)])$

Paso 1.4.3.2

Mueve $2$ a la izquierda de $\sec (2 x) \tan (2 x)$ .

$\frac{1}{\sec (2 x) + \tan (2 x)} (2 \cdot (\sec (2 x) \tan (2 x)) + \frac{d}{d x} [\tan (2 x)])$

Paso 1.5

Diferencia con la regla de la cadena, que establece que $\frac{d}{d x} [f (g (x))]$ es $f' (g (x)) g' (x)$ donde $f (x) = \tan (x)$ y $g (x) = 2 x$ .

Toca para ver más pasos...

Paso 1.5.1

Para aplicar la regla de la cadena, establece $u_{3}$ como $2 x$ .

$\frac{1}{\sec (2 x) + \tan (2 x)} (2 \sec (2 x) \tan (2 x) + \frac{d}{d u_{3}} [\tan (u_{3})] \frac{d}{d x} [2 x])$

Paso 1.5.2

La derivada de $\tan (u_{3})$ con respecto a $u_{3}$ es $\sec^{2} (u_{3})$ .

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

Paso 1.5.3

Reemplaza todos los casos de $u_{3}$ con $2 x$ .

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

Paso 1.6

Diferencia.

Toca para ver más pasos...

Paso 1.6.1

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

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

Paso 1.6.2

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

$\frac{1}{\sec (2 x) + \tan (2 x)} (2 \sec (2 x) \tan (2 x) + \sec^{2} (2 x) (2 \cdot 1))$

Paso 1.6.3

Simplifica la expresión.

Toca para ver más pasos...

Paso 1.6.3.1

Multiplica $2$ por $1$ .

$\frac{1}{\sec (2 x) + \tan (2 x)} (2 \sec (2 x) \tan (2 x) + \sec^{2} (2 x) \cdot 2)$

Paso 1.6.3.2

Mueve $2$ a la izquierda de $\sec^{2} (2 x)$ .

$\frac{1}{\sec (2 x) + \tan (2 x)} (2 \sec (2 x) \tan (2 x) + 2 \cdot \sec^{2} (2 x))$

Paso 1.7

Simplifica.

Toca para ver más pasos...

Paso 1.7.1

Reordena los factores de $\frac{1}{\sec (2 x) + \tan (2 x)} (2 \sec (2 x) \tan (2 x) + 2 \sec^{2} (2 x))$ .

$(2 \sec (2 x) \tan (2 x) + 2 \sec^{2} (2 x)) \frac{1}{\sec (2 x) + \tan (2 x)}$

Paso 1.7.2

Aplica la propiedad distributiva.

$2 \sec (2 x) \tan (2 x) \frac{1}{\sec (2 x) + \tan (2 x)} + 2 \sec^{2} (2 x) \frac{1}{\sec (2 x) + \tan (2 x)}$

Paso 1.7.3

Multiplica $2 \sec (2 x) \tan (2 x) \frac{1}{\sec (2 x) + \tan (2 x)}$ .

Toca para ver más pasos...

Paso 1.7.3.1

Combina $\frac{1}{\sec (2 x) + \tan (2 x)}$ y $2$ .

$\frac{2}{\sec (2 x) + \tan (2 x)} \sec (2 x) \tan (2 x) + 2 \sec^{2} (2 x) \frac{1}{\sec (2 x) + \tan (2 x)}$

Paso 1.7.3.2

Combina $\frac{2}{\sec (2 x) + \tan (2 x)}$ y $\sec (2 x)$ .

$\frac{2 \sec (2 x)}{\sec (2 x) + \tan (2 x)} \tan (2 x) + 2 \sec^{2} (2 x) \frac{1}{\sec (2 x) + \tan (2 x)}$

Paso 1.7.3.3

Combina $\frac{2 \sec (2 x)}{\sec (2 x) + \tan (2 x)}$ y $\tan (2 x)$ .

$\frac{2 \sec (2 x) \tan (2 x)}{\sec (2 x) + \tan (2 x)} + 2 \sec^{2} (2 x) \frac{1}{\sec (2 x) + \tan (2 x)}$

Paso 1.7.4

Multiplica $2 \sec^{2} (2 x) \frac{1}{\sec (2 x) + \tan (2 x)}$ .

Toca para ver más pasos...

Paso 1.7.4.1

Combina $\frac{1}{\sec (2 x) + \tan (2 x)}$ y $2$ .

$\frac{2 \sec (2 x) \tan (2 x)}{\sec (2 x) + \tan (2 x)} + \frac{2}{\sec (2 x) + \tan (2 x)} \sec^{2} (2 x)$

Paso 1.7.4.2

Combina $\frac{2}{\sec (2 x) + \tan (2 x)}$ y $\sec^{2} (2 x)$ .

$\frac{2 \sec (2 x) \tan (2 x)}{\sec (2 x) + \tan (2 x)} + \frac{2 \sec^{2} (2 x)}{\sec (2 x) + \tan (2 x)}$

Paso 1.7.5

Combina los numeradores sobre el denominador común.

$\frac{2 \sec (2 x) \tan (2 x) + 2 \sec^{2} (2 x)}{\sec (2 x) + \tan (2 x)}$

Paso 1.7.6

Factoriza $2 \sec (2 x)$ de $2 \sec (2 x) \tan (2 x) + 2 \sec^{2} (2 x)$ .

Toca para ver más pasos...

Paso 1.7.6.1

Factoriza $2 \sec (2 x)$ de $2 \sec (2 x) \tan (2 x)$ .

$\frac{2 \sec (2 x) (\tan (2 x)) + 2 \sec^{2} (2 x)}{\sec (2 x) + \tan (2 x)}$

Paso 1.7.6.2

Factoriza $2 \sec (2 x)$ de $2 \sec^{2} (2 x)$ .

$\frac{2 \sec (2 x) (\tan (2 x)) + 2 \sec (2 x) (\sec (2 x))}{\sec (2 x) + \tan (2 x)}$

Paso 1.7.6.3

Factoriza $2 \sec (2 x)$ de $2 \sec (2 x) (\tan (2 x)) + 2 \sec (2 x) (\sec (2 x))$ .

$f' (x) = \frac{2 \sec (2 x) (\tan (2 x) + \sec (2 x))}{\sec (2 x) + \tan (2 x)}$

Paso 2

Obtener la segunda derivada.

Toca para ver más pasos...

Paso 2.1

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

$2 \frac{d}{d x} [\frac{\sec (2 x) (\tan (2 x) + \sec (2 x))}{\sec (2 x) + \tan (2 x)}]$

Paso 2.2

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 $f (x) = \sec (2 x) (\tan (2 x) + \sec (2 x))$ y $g (x) = \sec (2 x) + \tan (2 x)$ .

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

Paso 2.3

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 $f (x) = \sec (2 x)$ y $g (x) = \tan (2 x) + \sec (2 x)$ .

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

Paso 2.4

Según la regla de la suma, la derivada de $\tan (2 x) + \sec (2 x)$ con respecto a $x$ es $\frac{d}{d x} [\tan (2 x)] + \frac{d}{d x} [\sec (2 x)]$ .

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

Paso 2.5

Diferencia con la regla de la cadena, que establece que $\frac{d}{d x} [f (g (x))]$ es $f' (g (x)) g' (x)$ donde $f (x) = \tan (x)$ y $g (x) = 2 x$ .

Toca para ver más pasos...

Paso 2.5.1

Para aplicar la regla de la cadena, establece $u_{1}$ como $2 x$ .

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

Paso 2.5.2

La derivada de $\tan (u_{1})$ con respecto a $u_{1}$ es $\sec^{2} (u_{1})$ .

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

Paso 2.5.3

Reemplaza todos los casos de $u_{1}$ con $2 x$ .

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

Paso 2.6

Diferencia.

Toca para ver más pasos...

Paso 2.6.1

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

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

Paso 2.6.2

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

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

Paso 2.6.3

Simplifica la expresión.

Toca para ver más pasos...

Paso 2.6.3.1

Multiplica $2$ por $1$ .

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

Paso 2.6.3.2

Mueve $2$ a la izquierda de $\sec^{2} (2 x)$ .

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

Paso 2.7

Diferencia con la regla de la cadena, que establece que $\frac{d}{d x} [f (g (x))]$ es $f' (g (x)) g' (x)$ donde $f (x) = \sec (x)$ y $g (x) = 2 x$ .

Toca para ver más pasos...

Paso 2.7.1

Para aplicar la regla de la cadena, establece $u_{2}$ como $2 x$ .

$2 \frac{(\sec (2 x) + \tan (2 x)) (\sec (2 x) (2 \sec^{2} (2 x) + \frac{d}{d u_{2}} [\sec (u_{2})] \frac{d}{d x} [2 x]) + (\tan (2 x) + \sec (2 x)) \frac{d}{d x} [\sec (2 x)]) - \sec (2 x) (\tan (2 x) + \sec (2 x)) \frac{d}{d x} [\sec (2 x) + \tan (2 x)]}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.7.2

La derivada de $\sec (u_{2})$ con respecto a $u_{2}$ es $\sec (u_{2}) \tan (u_{2})$ .

$2 \frac{(\sec (2 x) + \tan (2 x)) (\sec (2 x) (2 \sec^{2} (2 x) + \sec (u_{2}) \tan (u_{2}) \frac{d}{d x} [2 x]) + (\tan (2 x) + \sec (2 x)) \frac{d}{d x} [\sec (2 x)]) - \sec (2 x) (\tan (2 x) + \sec (2 x)) \frac{d}{d x} [\sec (2 x) + \tan (2 x)]}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.7.3

Reemplaza todos los casos de $u_{2}$ con $2 x$ .

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

Paso 2.8

Diferencia.

Toca para ver más pasos...

Paso 2.8.1

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

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

Paso 2.8.2

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

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

Paso 2.8.3

Simplifica la expresión.

Toca para ver más pasos...

Paso 2.8.3.1

Multiplica $2$ por $1$ .

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

Paso 2.8.3.2

Mueve $2$ a la izquierda de $\sec (2 x) \tan (2 x)$ .

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

Paso 2.9

Diferencia con la regla de la cadena, que establece que $\frac{d}{d x} [f (g (x))]$ es $f' (g (x)) g' (x)$ donde $f (x) = \sec (x)$ y $g (x) = 2 x$ .

Toca para ver más pasos...

Paso 2.9.1

Para aplicar la regla de la cadena, establece $u_{3}$ como $2 x$ .

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

Paso 2.9.2

La derivada de $\sec (u_{3})$ con respecto a $u_{3}$ es $\sec (u_{3}) \tan (u_{3})$ .

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

Paso 2.9.3

Reemplaza todos los casos de $u_{3}$ con $2 x$ .

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

Paso 2.10

Diferencia.

Toca para ver más pasos...

Paso 2.10.1

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

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

Paso 2.10.2

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

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

Paso 2.10.3

Simplifica la expresión.

Toca para ver más pasos...

Paso 2.10.3.1

Multiplica $2$ por $1$ .

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

Paso 2.10.3.2

Mueve $2$ a la izquierda de $(\tan (2 x) + \sec (2 x)) \sec (2 x) \tan (2 x)$ .

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

Paso 2.10.4

Según la regla de la suma, la derivada de $\sec (2 x) + \tan (2 x)$ con respecto a $x$ es $\frac{d}{d x} [\sec (2 x)] + \frac{d}{d x} [\tan (2 x)]$ .

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

Paso 2.11

Diferencia con la regla de la cadena, que establece que $\frac{d}{d x} [f (g (x))]$ es $f' (g (x)) g' (x)$ donde $f (x) = \sec (x)$ y $g (x) = 2 x$ .

Toca para ver más pasos...

Paso 2.11.1

Para aplicar la regla de la cadena, establece $u_{4}$ como $2 x$ .

$2 \frac{(\sec (2 x) + \tan (2 x)) (\sec (2 x) (2 \sec^{2} (2 x) + 2 \sec (2 x) \tan (2 x)) + 2 (\tan (2 x) + \sec (2 x)) \sec (2 x) \tan (2 x)) - \sec (2 x) (\tan (2 x) + \sec (2 x)) (\frac{d}{d u_{4}} [\sec (u_{4})] \frac{d}{d x} [2 x] + \frac{d}{d x} [\tan (2 x)])}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.11.2

La derivada de $\sec (u_{4})$ con respecto a $u_{4}$ es $\sec (u_{4}) \tan (u_{4})$ .

$2 \frac{(\sec (2 x) + \tan (2 x)) (\sec (2 x) (2 \sec^{2} (2 x) + 2 \sec (2 x) \tan (2 x)) + 2 (\tan (2 x) + \sec (2 x)) \sec (2 x) \tan (2 x)) - \sec (2 x) (\tan (2 x) + \sec (2 x)) (\sec (u_{4}) \tan (u_{4}) \frac{d}{d x} [2 x] + \frac{d}{d x} [\tan (2 x)])}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.11.3

Reemplaza todos los casos de $u_{4}$ con $2 x$ .

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

Paso 2.12

Diferencia.

Toca para ver más pasos...

Paso 2.12.1

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

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

Paso 2.12.2

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

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

Paso 2.12.3

Simplifica la expresión.

Toca para ver más pasos...

Paso 2.12.3.1

Multiplica $2$ por $1$ .

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

Paso 2.12.3.2

Mueve $2$ a la izquierda de $\sec (2 x) \tan (2 x)$ .

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

Paso 2.13

Diferencia con la regla de la cadena, que establece que $\frac{d}{d x} [f (g (x))]$ es $f' (g (x)) g' (x)$ donde $f (x) = \tan (x)$ y $g (x) = 2 x$ .

Toca para ver más pasos...

Paso 2.13.1

Para aplicar la regla de la cadena, establece $u_{5}$ como $2 x$ .

$2 \frac{(\sec (2 x) + \tan (2 x)) (\sec (2 x) (2 \sec^{2} (2 x) + 2 \sec (2 x) \tan (2 x)) + 2 (\tan (2 x) + \sec (2 x)) \sec (2 x) \tan (2 x)) - \sec (2 x) (\tan (2 x) + \sec (2 x)) (2 \sec (2 x) \tan (2 x) + \frac{d}{d u_{5}} [\tan (u_{5})] \frac{d}{d x} [2 x])}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.13.2

La derivada de $\tan (u_{5})$ con respecto a $u_{5}$ es $\sec^{2} (u_{5})$ .

$2 \frac{(\sec (2 x) + \tan (2 x)) (\sec (2 x) (2 \sec^{2} (2 x) + 2 \sec (2 x) \tan (2 x)) + 2 (\tan (2 x) + \sec (2 x)) \sec (2 x) \tan (2 x)) - \sec (2 x) (\tan (2 x) + \sec (2 x)) (2 \sec (2 x) \tan (2 x) + \sec^{2} (u_{5}) \frac{d}{d x} [2 x])}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.13.3

Reemplaza todos los casos de $u_{5}$ con $2 x$ .

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

Paso 2.14

Diferencia.

Toca para ver más pasos...

Paso 2.14.1

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

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

Paso 2.14.2

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

$2 \frac{(\sec (2 x) + \tan (2 x)) (\sec (2 x) (2 \sec^{2} (2 x) + 2 \sec (2 x) \tan (2 x)) + 2 (\tan (2 x) + \sec (2 x)) \sec (2 x) \tan (2 x)) - \sec (2 x) (\tan (2 x) + \sec (2 x)) (2 \sec (2 x) \tan (2 x) + \sec^{2} (2 x) (2 \cdot 1))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.14.3

Combina fracciones.

Toca para ver más pasos...

Paso 2.14.3.1

Multiplica $2$ por $1$ .

$2 \frac{(\sec (2 x) + \tan (2 x)) (\sec (2 x) (2 \sec^{2} (2 x) + 2 \sec (2 x) \tan (2 x)) + 2 (\tan (2 x) + \sec (2 x)) \sec (2 x) \tan (2 x)) - \sec (2 x) (\tan (2 x) + \sec (2 x)) (2 \sec (2 x) \tan (2 x) + \sec^{2} (2 x) \cdot 2)}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.14.3.2

Mueve $2$ a la izquierda de $\sec^{2} (2 x)$ .

$2 \frac{(\sec (2 x) + \tan (2 x)) (\sec (2 x) (2 \sec^{2} (2 x) + 2 \sec (2 x) \tan (2 x)) + 2 (\tan (2 x) + \sec (2 x)) \sec (2 x) \tan (2 x)) - \sec (2 x) (\tan (2 x) + \sec (2 x)) (2 \sec (2 x) \tan (2 x) + 2 \cdot \sec^{2} (2 x))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.14.3.3

Combina $2$ y $\frac{(\sec (2 x) + \tan (2 x)) (\sec (2 x) (2 \sec^{2} (2 x) + 2 \sec (2 x) \tan (2 x)) + 2 (\tan (2 x) + \sec (2 x)) \sec (2 x) \tan (2 x)) - \sec (2 x) (\tan (2 x) + \sec (2 x)) (2 \sec (2 x) \tan (2 x) + 2 \sec^{2} (2 x))}{{(\sec (2 x) + \tan (2 x))}^{2}}$ .

$\frac{2 ((\sec (2 x) + \tan (2 x)) (\sec (2 x) (2 \sec^{2} (2 x) + 2 \sec (2 x) \tan (2 x)) + 2 (\tan (2 x) + \sec (2 x)) \sec (2 x) \tan (2 x)) - \sec (2 x) (\tan (2 x) + \sec (2 x)) (2 \sec (2 x) \tan (2 x) + 2 \sec^{2} (2 x)))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15

Simplifica.

Toca para ver más pasos...

Paso 2.15.1

Aplica la propiedad distributiva.

$\frac{2 ((\sec (2 x) + \tan (2 x)) (\sec (2 x) (2 \sec^{2} (2 x)) + \sec (2 x) (2 \sec (2 x) \tan (2 x)) + 2 (\tan (2 x) + \sec (2 x)) \sec (2 x) \tan (2 x)) - \sec (2 x) (\tan (2 x) + \sec (2 x)) (2 \sec (2 x) \tan (2 x) + 2 \sec^{2} (2 x)))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.2

Aplica la propiedad distributiva.

$\frac{2 ((\sec (2 x) + \tan (2 x)) (\sec (2 x) (2 \sec^{2} (2 x)) + \sec (2 x) (2 \sec (2 x) \tan (2 x)) + (2 \tan (2 x) + 2 \sec (2 x)) \sec (2 x) \tan (2 x)) - \sec (2 x) (\tan (2 x) + \sec (2 x)) (2 \sec (2 x) \tan (2 x) + 2 \sec^{2} (2 x)))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.3

Aplica la propiedad distributiva.

$\frac{2 ((\sec (2 x) + \tan (2 x)) (\sec (2 x) (2 \sec^{2} (2 x)) + \sec (2 x) (2 \sec (2 x) \tan (2 x)) + (2 \tan (2 x) \sec (2 x) + 2 \sec (2 x) \sec (2 x)) \tan (2 x)) - \sec (2 x) (\tan (2 x) + \sec (2 x)) (2 \sec (2 x) \tan (2 x) + 2 \sec^{2} (2 x)))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.4

Aplica la propiedad distributiva.

$\frac{2 ((\sec (2 x) + \tan (2 x)) (\sec (2 x) (2 \sec^{2} (2 x)) + \sec (2 x) (2 \sec (2 x) \tan (2 x)) + 2 \tan (2 x) \sec (2 x) \tan (2 x) + 2 \sec (2 x) \sec (2 x) \tan (2 x)) - \sec (2 x) (\tan (2 x) + \sec (2 x)) (2 \sec (2 x) \tan (2 x) + 2 \sec^{2} (2 x)))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.5

Aplica la propiedad distributiva.

$\frac{2 ((\sec (2 x) + \tan (2 x)) (\sec (2 x) (2 \sec^{2} (2 x)) + \sec (2 x) (2 \sec (2 x) \tan (2 x)) + 2 \tan (2 x) \sec (2 x) \tan (2 x) + 2 \sec (2 x) \sec (2 x) \tan (2 x)) + (- \sec (2 x) \tan (2 x) - \sec (2 x) \sec (2 x)) (2 \sec (2 x) \tan (2 x) + 2 \sec^{2} (2 x)))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.6

Aplica la propiedad distributiva.

$\frac{2 ((\sec (2 x) + \tan (2 x)) (\sec (2 x) (2 \sec^{2} (2 x)) + \sec (2 x) (2 \sec (2 x) \tan (2 x)) + 2 \tan (2 x) \sec (2 x) \tan (2 x) + 2 \sec (2 x) \sec (2 x) \tan (2 x))) + 2 ((- \sec (2 x) \tan (2 x) - \sec (2 x) \sec (2 x)) (2 \sec (2 x) \tan (2 x) + 2 \sec^{2} (2 x)))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.7

Simplifica el numerador.

Toca para ver más pasos...

Paso 2.15.7.1

Simplifica cada término.

Toca para ver más pasos...

Paso 2.15.7.1.1

Simplifica cada término.

Toca para ver más pasos...

Paso 2.15.7.1.1.1

Reescribe con la propiedad conmutativa de la multiplicación.

$\frac{2 ((\sec (2 x) + \tan (2 x)) (2 \sec (2 x) \sec^{2} (2 x) + \sec (2 x) (2 \sec (2 x) \tan (2 x)) + 2 \tan (2 x) \sec (2 x) \tan (2 x) + 2 \sec (2 x) \sec (2 x) \tan (2 x))) + 2 ((- \sec (2 x) \tan (2 x) - \sec (2 x) \sec (2 x)) (2 \sec (2 x) \tan (2 x) + 2 \sec^{2} (2 x)))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.7.1.1.2

Multiplica $\sec (2 x)$ por $\sec^{2} (2 x)$ sumando los exponentes.

Toca para ver más pasos...

Paso 2.15.7.1.1.2.1

Mueve $\sec^{2} (2 x)$ .

$\frac{2 ((\sec (2 x) + \tan (2 x)) (2 (\sec^{2} (2 x) \sec (2 x)) + \sec (2 x) (2 \sec (2 x) \tan (2 x)) + 2 \tan (2 x) \sec (2 x) \tan (2 x) + 2 \sec (2 x) \sec (2 x) \tan (2 x))) + 2 ((- \sec (2 x) \tan (2 x) - \sec (2 x) \sec (2 x)) (2 \sec (2 x) \tan (2 x) + 2 \sec^{2} (2 x)))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.7.1.1.2.2

Multiplica $\sec^{2} (2 x)$ por $\sec (2 x)$ .

Toca para ver más pasos...

Paso 2.15.7.1.1.2.2.1

Eleva $\sec (2 x)$ a la potencia de $1$ .

$\frac{2 ((\sec (2 x) + \tan (2 x)) (2 (\sec^{2} (2 x) \sec^{1} (2 x)) + \sec (2 x) (2 \sec (2 x) \tan (2 x)) + 2 \tan (2 x) \sec (2 x) \tan (2 x) + 2 \sec (2 x) \sec (2 x) \tan (2 x))) + 2 ((- \sec (2 x) \tan (2 x) - \sec (2 x) \sec (2 x)) (2 \sec (2 x) \tan (2 x) + 2 \sec^{2} (2 x)))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.7.1.1.2.2.2

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

$\frac{2 ((\sec (2 x) + \tan (2 x)) (2 {\sec (2 x)}^{2 + 1} + \sec (2 x) (2 \sec (2 x) \tan (2 x)) + 2 \tan (2 x) \sec (2 x) \tan (2 x) + 2 \sec (2 x) \sec (2 x) \tan (2 x))) + 2 ((- \sec (2 x) \tan (2 x) - \sec (2 x) \sec (2 x)) (2 \sec (2 x) \tan (2 x) + 2 \sec^{2} (2 x)))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.7.1.1.2.3

Suma $2$ y $1$ .

$\frac{2 ((\sec (2 x) + \tan (2 x)) (2 \sec^{3} (2 x) + \sec (2 x) (2 \sec (2 x) \tan (2 x)) + 2 \tan (2 x) \sec (2 x) \tan (2 x) + 2 \sec (2 x) \sec (2 x) \tan (2 x))) + 2 ((- \sec (2 x) \tan (2 x) - \sec (2 x) \sec (2 x)) (2 \sec (2 x) \tan (2 x) + 2 \sec^{2} (2 x)))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.7.1.1.3

Reescribe con la propiedad conmutativa de la multiplicación.

$\frac{2 ((\sec (2 x) + \tan (2 x)) (2 \sec^{3} (2 x) + 2 \sec (2 x) \sec (2 x) \tan (2 x) + 2 \tan (2 x) \sec (2 x) \tan (2 x) + 2 \sec (2 x) \sec (2 x) \tan (2 x))) + 2 ((- \sec (2 x) \tan (2 x) - \sec (2 x) \sec (2 x)) (2 \sec (2 x) \tan (2 x) + 2 \sec^{2} (2 x)))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.7.1.1.4

Multiplica $2 \sec (2 x) \sec (2 x)$ .

Toca para ver más pasos...

Paso 2.15.7.1.1.4.1

Eleva $\sec (2 x)$ a la potencia de $1$ .

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

Paso 2.15.7.1.1.4.2

Eleva $\sec (2 x)$ a la potencia de $1$ .

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

Paso 2.15.7.1.1.4.3

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

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

Paso 2.15.7.1.1.4.4

Suma $1$ y $1$ .

$\frac{2 ((\sec (2 x) + \tan (2 x)) (2 \sec^{3} (2 x) + 2 \sec^{2} (2 x) \tan (2 x) + 2 \tan (2 x) \sec (2 x) \tan (2 x) + 2 \sec (2 x) \sec (2 x) \tan (2 x))) + 2 ((- \sec (2 x) \tan (2 x) - \sec (2 x) \sec (2 x)) (2 \sec (2 x) \tan (2 x) + 2 \sec^{2} (2 x)))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.7.1.1.5

Multiplica $2 \tan (2 x) \sec (2 x) \tan (2 x)$ .

Toca para ver más pasos...

Paso 2.15.7.1.1.5.1

Eleva $\tan (2 x)$ a la potencia de $1$ .

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

Paso 2.15.7.1.1.5.2

Eleva $\tan (2 x)$ a la potencia de $1$ .

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

Paso 2.15.7.1.1.5.3

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

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

Paso 2.15.7.1.1.5.4

Suma $1$ y $1$ .

$\frac{2 ((\sec (2 x) + \tan (2 x)) (2 \sec^{3} (2 x) + 2 \sec^{2} (2 x) \tan (2 x) + 2 \tan^{2} (2 x) \sec (2 x) + 2 \sec (2 x) \sec (2 x) \tan (2 x))) + 2 ((- \sec (2 x) \tan (2 x) - \sec (2 x) \sec (2 x)) (2 \sec (2 x) \tan (2 x) + 2 \sec^{2} (2 x)))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.7.1.1.6

Multiplica $2 \sec (2 x) \sec (2 x)$ .

Toca para ver más pasos...

Paso 2.15.7.1.1.6.1

Eleva $\sec (2 x)$ a la potencia de $1$ .

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

Paso 2.15.7.1.1.6.2

Eleva $\sec (2 x)$ a la potencia de $1$ .

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

Paso 2.15.7.1.1.6.3

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

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

Paso 2.15.7.1.1.6.4

Suma $1$ y $1$ .

$\frac{2 ((\sec (2 x) + \tan (2 x)) (2 \sec^{3} (2 x) + 2 \sec^{2} (2 x) \tan (2 x) + 2 \tan^{2} (2 x) \sec (2 x) + 2 \sec^{2} (2 x) \tan (2 x))) + 2 ((- \sec (2 x) \tan (2 x) - \sec (2 x) \sec (2 x)) (2 \sec (2 x) \tan (2 x) + 2 \sec^{2} (2 x)))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.7.1.2

Suma $2 \sec^{2} (2 x) \tan (2 x)$ y $2 \sec^{2} (2 x) \tan (2 x)$ .

$\frac{2 ((\sec (2 x) + \tan (2 x)) (2 \sec^{3} (2 x) + 4 \sec^{2} (2 x) \tan (2 x) + 2 \tan^{2} (2 x) \sec (2 x))) + 2 ((- \sec (2 x) \tan (2 x) - \sec (2 x) \sec (2 x)) (2 \sec (2 x) \tan (2 x) + 2 \sec^{2} (2 x)))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.7.1.3

Expande $(\sec (2 x) + \tan (2 x)) (2 \sec^{3} (2 x) + 4 \sec^{2} (2 x) \tan (2 x) + 2 \tan^{2} (2 x) \sec (2 x))$ mediante la multiplicación de cada término de la primera expresión por cada término de la segunda expresión.

$\frac{2 (\sec (2 x) (2 \sec^{3} (2 x)) + \sec (2 x) (4 \sec^{2} (2 x) \tan (2 x)) + \sec (2 x) (2 \tan^{2} (2 x) \sec (2 x)) + \tan (2 x) (2 \sec^{3} (2 x)) + \tan (2 x) (4 \sec^{2} (2 x) \tan (2 x)) + \tan (2 x) (2 \tan^{2} (2 x) \sec (2 x))) + 2 ((- \sec (2 x) \tan (2 x) - \sec (2 x) \sec (2 x)) (2 \sec (2 x) \tan (2 x) + 2 \sec^{2} (2 x)))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.7.1.4

Simplifica cada término.

Toca para ver más pasos...

Paso 2.15.7.1.4.1

Reescribe con la propiedad conmutativa de la multiplicación.

$\frac{2 (2 \sec (2 x) \sec^{3} (2 x) + \sec (2 x) (4 \sec^{2} (2 x) \tan (2 x)) + \sec (2 x) (2 \tan^{2} (2 x) \sec (2 x)) + \tan (2 x) (2 \sec^{3} (2 x)) + \tan (2 x) (4 \sec^{2} (2 x) \tan (2 x)) + \tan (2 x) (2 \tan^{2} (2 x) \sec (2 x))) + 2 ((- \sec (2 x) \tan (2 x) - \sec (2 x) \sec (2 x)) (2 \sec (2 x) \tan (2 x) + 2 \sec^{2} (2 x)))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.7.1.4.2

Multiplica $\sec (2 x)$ por $\sec^{3} (2 x)$ sumando los exponentes.

Toca para ver más pasos...

Paso 2.15.7.1.4.2.1

Mueve $\sec^{3} (2 x)$ .

$\frac{2 (2 (\sec^{3} (2 x) \sec (2 x)) + \sec (2 x) (4 \sec^{2} (2 x) \tan (2 x)) + \sec (2 x) (2 \tan^{2} (2 x) \sec (2 x)) + \tan (2 x) (2 \sec^{3} (2 x)) + \tan (2 x) (4 \sec^{2} (2 x) \tan (2 x)) + \tan (2 x) (2 \tan^{2} (2 x) \sec (2 x))) + 2 ((- \sec (2 x) \tan (2 x) - \sec (2 x) \sec (2 x)) (2 \sec (2 x) \tan (2 x) + 2 \sec^{2} (2 x)))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.7.1.4.2.2

Multiplica $\sec^{3} (2 x)$ por $\sec (2 x)$ .

Toca para ver más pasos...

Paso 2.15.7.1.4.2.2.1

Eleva $\sec (2 x)$ a la potencia de $1$ .

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

Paso 2.15.7.1.4.2.2.2

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

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

Paso 2.15.7.1.4.2.3

Suma $3$ y $1$ .

$\frac{2 (2 \sec^{4} (2 x) + \sec (2 x) (4 \sec^{2} (2 x) \tan (2 x)) + \sec (2 x) (2 \tan^{2} (2 x) \sec (2 x)) + \tan (2 x) (2 \sec^{3} (2 x)) + \tan (2 x) (4 \sec^{2} (2 x) \tan (2 x)) + \tan (2 x) (2 \tan^{2} (2 x) \sec (2 x))) + 2 ((- \sec (2 x) \tan (2 x) - \sec (2 x) \sec (2 x)) (2 \sec (2 x) \tan (2 x) + 2 \sec^{2} (2 x)))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.7.1.4.3

Reescribe con la propiedad conmutativa de la multiplicación.

$\frac{2 (2 \sec^{4} (2 x) + 4 \sec (2 x) \sec^{2} (2 x) \tan (2 x) + \sec (2 x) (2 \tan^{2} (2 x) \sec (2 x)) + \tan (2 x) (2 \sec^{3} (2 x)) + \tan (2 x) (4 \sec^{2} (2 x) \tan (2 x)) + \tan (2 x) (2 \tan^{2} (2 x) \sec (2 x))) + 2 ((- \sec (2 x) \tan (2 x) - \sec (2 x) \sec (2 x)) (2 \sec (2 x) \tan (2 x) + 2 \sec^{2} (2 x)))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.7.1.4.4

Multiplica $\sec (2 x)$ por $\sec^{2} (2 x)$ sumando los exponentes.

Toca para ver más pasos...

Paso 2.15.7.1.4.4.1

Mueve $\sec^{2} (2 x)$ .

$\frac{2 (2 \sec^{4} (2 x) + 4 (\sec^{2} (2 x) \sec (2 x)) \tan (2 x) + \sec (2 x) (2 \tan^{2} (2 x) \sec (2 x)) + \tan (2 x) (2 \sec^{3} (2 x)) + \tan (2 x) (4 \sec^{2} (2 x) \tan (2 x)) + \tan (2 x) (2 \tan^{2} (2 x) \sec (2 x))) + 2 ((- \sec (2 x) \tan (2 x) - \sec (2 x) \sec (2 x)) (2 \sec (2 x) \tan (2 x) + 2 \sec^{2} (2 x)))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.7.1.4.4.2

Multiplica $\sec^{2} (2 x)$ por $\sec (2 x)$ .

Toca para ver más pasos...

Paso 2.15.7.1.4.4.2.1

Eleva $\sec (2 x)$ a la potencia de $1$ .

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

Paso 2.15.7.1.4.4.2.2

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

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

Paso 2.15.7.1.4.4.3

Suma $2$ y $1$ .

$\frac{2 (2 \sec^{4} (2 x) + 4 \sec^{3} (2 x) \tan (2 x) + \sec (2 x) (2 \tan^{2} (2 x) \sec (2 x)) + \tan (2 x) (2 \sec^{3} (2 x)) + \tan (2 x) (4 \sec^{2} (2 x) \tan (2 x)) + \tan (2 x) (2 \tan^{2} (2 x) \sec (2 x))) + 2 ((- \sec (2 x) \tan (2 x) - \sec (2 x) \sec (2 x)) (2 \sec (2 x) \tan (2 x) + 2 \sec^{2} (2 x)))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.7.1.4.5

Reescribe con la propiedad conmutativa de la multiplicación.

$\frac{2 (2 \sec^{4} (2 x) + 4 \sec^{3} (2 x) \tan (2 x) + 2 \sec (2 x) \tan^{2} (2 x) \sec (2 x) + \tan (2 x) (2 \sec^{3} (2 x)) + \tan (2 x) (4 \sec^{2} (2 x) \tan (2 x)) + \tan (2 x) (2 \tan^{2} (2 x) \sec (2 x))) + 2 ((- \sec (2 x) \tan (2 x) - \sec (2 x) \sec (2 x)) (2 \sec (2 x) \tan (2 x) + 2 \sec^{2} (2 x)))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.7.1.4.6

Multiplica $2 \sec (2 x) \tan^{2} (2 x) \sec (2 x)$ .

Toca para ver más pasos...

Paso 2.15.7.1.4.6.1

Eleva $\sec (2 x)$ a la potencia de $1$ .

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

Paso 2.15.7.1.4.6.2

Eleva $\sec (2 x)$ a la potencia de $1$ .

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

Paso 2.15.7.1.4.6.3

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

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

Paso 2.15.7.1.4.6.4

Suma $1$ y $1$ .

$\frac{2 (2 \sec^{4} (2 x) + 4 \sec^{3} (2 x) \tan (2 x) + 2 \sec^{2} (2 x) \tan^{2} (2 x) + \tan (2 x) (2 \sec^{3} (2 x)) + \tan (2 x) (4 \sec^{2} (2 x) \tan (2 x)) + \tan (2 x) (2 \tan^{2} (2 x) \sec (2 x))) + 2 ((- \sec (2 x) \tan (2 x) - \sec (2 x) \sec (2 x)) (2 \sec (2 x) \tan (2 x) + 2 \sec^{2} (2 x)))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.7.1.4.7

Reescribe con la propiedad conmutativa de la multiplicación.

$\frac{2 (2 \sec^{4} (2 x) + 4 \sec^{3} (2 x) \tan (2 x) + 2 \sec^{2} (2 x) \tan^{2} (2 x) + 2 \tan (2 x) \sec^{3} (2 x) + \tan (2 x) (4 \sec^{2} (2 x) \tan (2 x)) + \tan (2 x) (2 \tan^{2} (2 x) \sec (2 x))) + 2 ((- \sec (2 x) \tan (2 x) - \sec (2 x) \sec (2 x)) (2 \sec (2 x) \tan (2 x) + 2 \sec^{2} (2 x)))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.7.1.4.8

Reescribe con la propiedad conmutativa de la multiplicación.

$\frac{2 (2 \sec^{4} (2 x) + 4 \sec^{3} (2 x) \tan (2 x) + 2 \sec^{2} (2 x) \tan^{2} (2 x) + 2 \tan (2 x) \sec^{3} (2 x) + 4 \tan (2 x) \sec^{2} (2 x) \tan (2 x) + \tan (2 x) (2 \tan^{2} (2 x) \sec (2 x))) + 2 ((- \sec (2 x) \tan (2 x) - \sec (2 x) \sec (2 x)) (2 \sec (2 x) \tan (2 x) + 2 \sec^{2} (2 x)))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.7.1.4.9

Multiplica $4 \tan (2 x) \sec^{2} (2 x) \tan (2 x)$ .

Toca para ver más pasos...

Paso 2.15.7.1.4.9.1

Eleva $\tan (2 x)$ a la potencia de $1$ .

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

Paso 2.15.7.1.4.9.2

Eleva $\tan (2 x)$ a la potencia de $1$ .

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

Paso 2.15.7.1.4.9.3

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

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

Paso 2.15.7.1.4.9.4

Suma $1$ y $1$ .

$\frac{2 (2 \sec^{4} (2 x) + 4 \sec^{3} (2 x) \tan (2 x) + 2 \sec^{2} (2 x) \tan^{2} (2 x) + 2 \tan (2 x) \sec^{3} (2 x) + 4 \tan^{2} (2 x) \sec^{2} (2 x) + \tan (2 x) (2 \tan^{2} (2 x) \sec (2 x))) + 2 ((- \sec (2 x) \tan (2 x) - \sec (2 x) \sec (2 x)) (2 \sec (2 x) \tan (2 x) + 2 \sec^{2} (2 x)))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.7.1.4.10

Reescribe con la propiedad conmutativa de la multiplicación.

$\frac{2 (2 \sec^{4} (2 x) + 4 \sec^{3} (2 x) \tan (2 x) + 2 \sec^{2} (2 x) \tan^{2} (2 x) + 2 \tan (2 x) \sec^{3} (2 x) + 4 \tan^{2} (2 x) \sec^{2} (2 x) + 2 \tan (2 x) \tan^{2} (2 x) \sec (2 x)) + 2 ((- \sec (2 x) \tan (2 x) - \sec (2 x) \sec (2 x)) (2 \sec (2 x) \tan (2 x) + 2 \sec^{2} (2 x)))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.7.1.4.11

Multiplica $\tan (2 x)$ por $\tan^{2} (2 x)$ sumando los exponentes.

Toca para ver más pasos...

Paso 2.15.7.1.4.11.1

Mueve $\tan^{2} (2 x)$ .

$\frac{2 (2 \sec^{4} (2 x) + 4 \sec^{3} (2 x) \tan (2 x) + 2 \sec^{2} (2 x) \tan^{2} (2 x) + 2 \tan (2 x) \sec^{3} (2 x) + 4 \tan^{2} (2 x) \sec^{2} (2 x) + 2 (\tan^{2} (2 x) \tan (2 x)) \sec (2 x)) + 2 ((- \sec (2 x) \tan (2 x) - \sec (2 x) \sec (2 x)) (2 \sec (2 x) \tan (2 x) + 2 \sec^{2} (2 x)))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.7.1.4.11.2

Multiplica $\tan^{2} (2 x)$ por $\tan (2 x)$ .

Toca para ver más pasos...

Paso 2.15.7.1.4.11.2.1

Eleva $\tan (2 x)$ a la potencia de $1$ .

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

Paso 2.15.7.1.4.11.2.2

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

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

Paso 2.15.7.1.4.11.3

Suma $2$ y $1$ .

$\frac{2 (2 \sec^{4} (2 x) + 4 \sec^{3} (2 x) \tan (2 x) + 2 \sec^{2} (2 x) \tan^{2} (2 x) + 2 \tan (2 x) \sec^{3} (2 x) + 4 \tan^{2} (2 x) \sec^{2} (2 x) + 2 \tan^{3} (2 x) \sec (2 x)) + 2 ((- \sec (2 x) \tan (2 x) - \sec (2 x) \sec (2 x)) (2 \sec (2 x) \tan (2 x) + 2 \sec^{2} (2 x)))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.7.1.5

Reordena los factores de $2 \tan (2 x) \sec^{3} (2 x)$ .

$\frac{2 (2 \sec^{4} (2 x) + 4 \sec^{3} (2 x) \tan (2 x) + 2 \sec^{2} (2 x) \tan^{2} (2 x) + 2 \sec^{3} (2 x) \tan (2 x) + 4 \tan^{2} (2 x) \sec^{2} (2 x) + 2 \tan^{3} (2 x) \sec (2 x)) + 2 ((- \sec (2 x) \tan (2 x) - \sec (2 x) \sec (2 x)) (2 \sec (2 x) \tan (2 x) + 2 \sec^{2} (2 x)))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.7.1.6

Suma $4 \sec^{3} (2 x) \tan (2 x)$ y $2 \sec^{3} (2 x) \tan (2 x)$ .

$\frac{2 (2 \sec^{4} (2 x) + 6 \sec^{3} (2 x) \tan (2 x) + 2 \sec^{2} (2 x) \tan^{2} (2 x) + 4 \tan^{2} (2 x) \sec^{2} (2 x) + 2 \tan^{3} (2 x) \sec (2 x)) + 2 ((- \sec (2 x) \tan (2 x) - \sec (2 x) \sec (2 x)) (2 \sec (2 x) \tan (2 x) + 2 \sec^{2} (2 x)))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.7.1.7

Reordena los factores de $4 \tan^{2} (2 x) \sec^{2} (2 x)$ .

$\frac{2 (2 \sec^{4} (2 x) + 6 \sec^{3} (2 x) \tan (2 x) + 2 \sec^{2} (2 x) \tan^{2} (2 x) + 4 \sec^{2} (2 x) \tan^{2} (2 x) + 2 \tan^{3} (2 x) \sec (2 x)) + 2 ((- \sec (2 x) \tan (2 x) - \sec (2 x) \sec (2 x)) (2 \sec (2 x) \tan (2 x) + 2 \sec^{2} (2 x)))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.7.1.8

Suma $2 \sec^{2} (2 x) \tan^{2} (2 x)$ y $4 \sec^{2} (2 x) \tan^{2} (2 x)$ .

$\frac{2 (2 \sec^{4} (2 x) + 6 \sec^{3} (2 x) \tan (2 x) + 6 \sec^{2} (2 x) \tan^{2} (2 x) + 2 \tan^{3} (2 x) \sec (2 x)) + 2 ((- \sec (2 x) \tan (2 x) - \sec (2 x) \sec (2 x)) (2 \sec (2 x) \tan (2 x) + 2 \sec^{2} (2 x)))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.7.1.9

Aplica la propiedad distributiva.

$\frac{2 (2 \sec^{4} (2 x)) + 2 (6 \sec^{3} (2 x) \tan (2 x)) + 2 (6 \sec^{2} (2 x) \tan^{2} (2 x)) + 2 (2 \tan^{3} (2 x) \sec (2 x)) + 2 ((- \sec (2 x) \tan (2 x) - \sec (2 x) \sec (2 x)) (2 \sec (2 x) \tan (2 x) + 2 \sec^{2} (2 x)))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.7.1.10

Simplifica.

Toca para ver más pasos...

Paso 2.15.7.1.10.1

Multiplica $2$ por $2$ .

$\frac{4 \sec^{4} (2 x) + 2 (6 \sec^{3} (2 x) \tan (2 x)) + 2 (6 \sec^{2} (2 x) \tan^{2} (2 x)) + 2 (2 \tan^{3} (2 x) \sec (2 x)) + 2 ((- \sec (2 x) \tan (2 x) - \sec (2 x) \sec (2 x)) (2 \sec (2 x) \tan (2 x) + 2 \sec^{2} (2 x)))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.7.1.10.2

Multiplica $6$ por $2$ .

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

Paso 2.15.7.1.10.3

Multiplica $6$ por $2$ .

$\frac{4 \sec^{4} (2 x) + 12 (\sec^{3} (2 x) \tan (2 x)) + 12 (\sec^{2} (2 x) \tan^{2} (2 x)) + 2 (2 \tan^{3} (2 x) \sec (2 x)) + 2 ((- \sec (2 x) \tan (2 x) - \sec (2 x) \sec (2 x)) (2 \sec (2 x) \tan (2 x) + 2 \sec^{2} (2 x)))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.7.1.10.4

Multiplica $2$ por $2$ .

$\frac{4 \sec^{4} (2 x) + 12 (\sec^{3} (2 x) \tan (2 x)) + 12 (\sec^{2} (2 x) \tan^{2} (2 x)) + 4 (\tan^{3} (2 x) \sec (2 x)) + 2 ((- \sec (2 x) \tan (2 x) - \sec (2 x) \sec (2 x)) (2 \sec (2 x) \tan (2 x) + 2 \sec^{2} (2 x)))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.7.1.11

Elimina los paréntesis.

$\frac{4 \sec^{4} (2 x) + 12 \sec^{3} (2 x) \tan (2 x) + 12 \sec^{2} (2 x) \tan^{2} (2 x) + 4 \tan^{3} (2 x) \sec (2 x) + 2 ((- \sec (2 x) \tan (2 x) - \sec (2 x) \sec (2 x)) (2 \sec (2 x) \tan (2 x) + 2 \sec^{2} (2 x)))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.7.1.12

Multiplica $- \sec (2 x) \sec (2 x)$ .

Toca para ver más pasos...

Paso 2.15.7.1.12.1

Eleva $\sec (2 x)$ a la potencia de $1$ .

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

Paso 2.15.7.1.12.2

Eleva $\sec (2 x)$ a la potencia de $1$ .

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

Paso 2.15.7.1.12.3

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

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

Paso 2.15.7.1.12.4

Suma $1$ y $1$ .

$\frac{4 \sec^{4} (2 x) + 12 \sec^{3} (2 x) \tan (2 x) + 12 \sec^{2} (2 x) \tan^{2} (2 x) + 4 \tan^{3} (2 x) \sec (2 x) + 2 ((- \sec (2 x) \tan (2 x) - \sec^{2} (2 x)) (2 \sec (2 x) \tan (2 x) + 2 \sec^{2} (2 x)))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.7.1.13

Expande $(- \sec (2 x) \tan (2 x) - \sec^{2} (2 x)) (2 \sec (2 x) \tan (2 x) + 2 \sec^{2} (2 x))$ con el método PEIU (primero, exterior, interior, ultimo).

Toca para ver más pasos...

Paso 2.15.7.1.13.1

Aplica la propiedad distributiva.

$\frac{4 \sec^{4} (2 x) + 12 \sec^{3} (2 x) \tan (2 x) + 12 \sec^{2} (2 x) \tan^{2} (2 x) + 4 \tan^{3} (2 x) \sec (2 x) + 2 (- \sec (2 x) \tan (2 x) (2 \sec (2 x) \tan (2 x) + 2 \sec^{2} (2 x)) - \sec^{2} (2 x) (2 \sec (2 x) \tan (2 x) + 2 \sec^{2} (2 x)))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.7.1.13.2

Aplica la propiedad distributiva.

$\frac{4 \sec^{4} (2 x) + 12 \sec^{3} (2 x) \tan (2 x) + 12 \sec^{2} (2 x) \tan^{2} (2 x) + 4 \tan^{3} (2 x) \sec (2 x) + 2 (- \sec (2 x) \tan (2 x) (2 \sec (2 x) \tan (2 x)) - \sec (2 x) \tan (2 x) (2 \sec^{2} (2 x)) - \sec^{2} (2 x) (2 \sec (2 x) \tan (2 x) + 2 \sec^{2} (2 x)))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.7.1.13.3

Aplica la propiedad distributiva.

$\frac{4 \sec^{4} (2 x) + 12 \sec^{3} (2 x) \tan (2 x) + 12 \sec^{2} (2 x) \tan^{2} (2 x) + 4 \tan^{3} (2 x) \sec (2 x) + 2 (- \sec (2 x) \tan (2 x) (2 \sec (2 x) \tan (2 x)) - \sec (2 x) \tan (2 x) (2 \sec^{2} (2 x)) - \sec^{2} (2 x) (2 \sec (2 x) \tan (2 x)) - \sec^{2} (2 x) (2 \sec^{2} (2 x)))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.7.1.14

Simplifica y combina los términos similares.

Toca para ver más pasos...

Paso 2.15.7.1.14.1

Simplifica cada término.

Toca para ver más pasos...

Paso 2.15.7.1.14.1.1

Multiplica $- \sec (2 x) \tan (2 x) (2 \sec (2 x) \tan (2 x))$ .

Toca para ver más pasos...

Paso 2.15.7.1.14.1.1.1

Multiplica $2$ por $- 1$ .

$\frac{4 \sec^{4} (2 x) + 12 \sec^{3} (2 x) \tan (2 x) + 12 \sec^{2} (2 x) \tan^{2} (2 x) + 4 \tan^{3} (2 x) \sec (2 x) + 2 (- 2 \sec (2 x) \tan (2 x) (\sec (2 x) \tan (2 x)) - \sec (2 x) \tan (2 x) (2 \sec^{2} (2 x)) - \sec^{2} (2 x) (2 \sec (2 x) \tan (2 x)) - \sec^{2} (2 x) (2 \sec^{2} (2 x)))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.7.1.14.1.1.2

Eleva $\sec (2 x)$ a la potencia de $1$ .

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

Paso 2.15.7.1.14.1.1.3

Eleva $\sec (2 x)$ a la potencia de $1$ .

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

Paso 2.15.7.1.14.1.1.4

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

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

Paso 2.15.7.1.14.1.1.5

Suma $1$ y $1$ .

$\frac{4 \sec^{4} (2 x) + 12 \sec^{3} (2 x) \tan (2 x) + 12 \sec^{2} (2 x) \tan^{2} (2 x) + 4 \tan^{3} (2 x) \sec (2 x) + 2 (- 2 \sec^{2} (2 x) \tan (2 x) \tan (2 x) - \sec (2 x) \tan (2 x) (2 \sec^{2} (2 x)) - \sec^{2} (2 x) (2 \sec (2 x) \tan (2 x)) - \sec^{2} (2 x) (2 \sec^{2} (2 x)))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.7.1.14.1.1.6

Eleva $\tan (2 x)$ a la potencia de $1$ .

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

Paso 2.15.7.1.14.1.1.7

Eleva $\tan (2 x)$ a la potencia de $1$ .

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

Paso 2.15.7.1.14.1.1.8

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

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

Paso 2.15.7.1.14.1.1.9

Suma $1$ y $1$ .

$\frac{4 \sec^{4} (2 x) + 12 \sec^{3} (2 x) \tan (2 x) + 12 \sec^{2} (2 x) \tan^{2} (2 x) + 4 \tan^{3} (2 x) \sec (2 x) + 2 (- 2 \sec^{2} (2 x) \tan^{2} (2 x) - \sec (2 x) \tan (2 x) (2 \sec^{2} (2 x)) - \sec^{2} (2 x) (2 \sec (2 x) \tan (2 x)) - \sec^{2} (2 x) (2 \sec^{2} (2 x)))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.7.1.14.1.2

Multiplica $\sec (2 x)$ por $\sec^{2} (2 x)$ sumando los exponentes.

Toca para ver más pasos...

Paso 2.15.7.1.14.1.2.1

Mueve $\sec^{2} (2 x)$ .

$\frac{4 \sec^{4} (2 x) + 12 \sec^{3} (2 x) \tan (2 x) + 12 \sec^{2} (2 x) \tan^{2} (2 x) + 4 \tan^{3} (2 x) \sec (2 x) + 2 (- 2 \sec^{2} (2 x) \tan^{2} (2 x) - (\sec^{2} (2 x) \sec (2 x)) \tan (2 x) \cdot 2 - \sec^{2} (2 x) (2 \sec (2 x) \tan (2 x)) - \sec^{2} (2 x) (2 \sec^{2} (2 x)))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.7.1.14.1.2.2

Multiplica $\sec^{2} (2 x)$ por $\sec (2 x)$ .

Toca para ver más pasos...

Paso 2.15.7.1.14.1.2.2.1

Eleva $\sec (2 x)$ a la potencia de $1$ .

$\frac{4 \sec^{4} (2 x) + 12 \sec^{3} (2 x) \tan (2 x) + 12 \sec^{2} (2 x) \tan^{2} (2 x) + 4 \tan^{3} (2 x) \sec (2 x) + 2 (- 2 \sec^{2} (2 x) \tan^{2} (2 x) - (\sec^{2} (2 x) \sec^{1} (2 x)) \tan (2 x) \cdot 2 - \sec^{2} (2 x) (2 \sec (2 x) \tan (2 x)) - \sec^{2} (2 x) (2 \sec^{2} (2 x)))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.7.1.14.1.2.2.2

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

$\frac{4 \sec^{4} (2 x) + 12 \sec^{3} (2 x) \tan (2 x) + 12 \sec^{2} (2 x) \tan^{2} (2 x) + 4 \tan^{3} (2 x) \sec (2 x) + 2 (- 2 \sec^{2} (2 x) \tan^{2} (2 x) - {\sec (2 x)}^{2 + 1} \tan (2 x) \cdot 2 - \sec^{2} (2 x) (2 \sec (2 x) \tan (2 x)) - \sec^{2} (2 x) (2 \sec^{2} (2 x)))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.7.1.14.1.2.3

Suma $2$ y $1$ .

$\frac{4 \sec^{4} (2 x) + 12 \sec^{3} (2 x) \tan (2 x) + 12 \sec^{2} (2 x) \tan^{2} (2 x) + 4 \tan^{3} (2 x) \sec (2 x) + 2 (- 2 \sec^{2} (2 x) \tan^{2} (2 x) - \sec^{3} (2 x) \tan (2 x) \cdot 2 - \sec^{2} (2 x) (2 \sec (2 x) \tan (2 x)) - \sec^{2} (2 x) (2 \sec^{2} (2 x)))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.7.1.14.1.3

Multiplica $2$ por $- 1$ .

$\frac{4 \sec^{4} (2 x) + 12 \sec^{3} (2 x) \tan (2 x) + 12 \sec^{2} (2 x) \tan^{2} (2 x) + 4 \tan^{3} (2 x) \sec (2 x) + 2 (- 2 \sec^{2} (2 x) \tan^{2} (2 x) - 2 \sec^{3} (2 x) \tan (2 x) - \sec^{2} (2 x) (2 \sec (2 x) \tan (2 x)) - \sec^{2} (2 x) (2 \sec^{2} (2 x)))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.7.1.14.1.4

Multiplica $\sec^{2} (2 x)$ por $\sec (2 x)$ sumando los exponentes.

Toca para ver más pasos...

Paso 2.15.7.1.14.1.4.1

Mueve $\sec (2 x)$ .

$\frac{4 \sec^{4} (2 x) + 12 \sec^{3} (2 x) \tan (2 x) + 12 \sec^{2} (2 x) \tan^{2} (2 x) + 4 \tan^{3} (2 x) \sec (2 x) + 2 (- 2 \sec^{2} (2 x) \tan^{2} (2 x) - 2 \sec^{3} (2 x) \tan (2 x) - (\sec (2 x) \sec^{2} (2 x)) (2 \tan (2 x)) - \sec^{2} (2 x) (2 \sec^{2} (2 x)))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.7.1.14.1.4.2

Multiplica $\sec (2 x)$ por $\sec^{2} (2 x)$ .

Toca para ver más pasos...

Paso 2.15.7.1.14.1.4.2.1

Eleva $\sec (2 x)$ a la potencia de $1$ .

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

Paso 2.15.7.1.14.1.4.2.2

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

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

Paso 2.15.7.1.14.1.4.3

Suma $1$ y $2$ .

$\frac{4 \sec^{4} (2 x) + 12 \sec^{3} (2 x) \tan (2 x) + 12 \sec^{2} (2 x) \tan^{2} (2 x) + 4 \tan^{3} (2 x) \sec (2 x) + 2 (- 2 \sec^{2} (2 x) \tan^{2} (2 x) - 2 \sec^{3} (2 x) \tan (2 x) - \sec^{3} (2 x) (2 \tan (2 x)) - \sec^{2} (2 x) (2 \sec^{2} (2 x)))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.7.1.14.1.5

Multiplica $2$ por $- 1$ .

$\frac{4 \sec^{4} (2 x) + 12 \sec^{3} (2 x) \tan (2 x) + 12 \sec^{2} (2 x) \tan^{2} (2 x) + 4 \tan^{3} (2 x) \sec (2 x) + 2 (- 2 \sec^{2} (2 x) \tan^{2} (2 x) - 2 \sec^{3} (2 x) \tan (2 x) - 2 \sec^{3} (2 x) \tan (2 x) - \sec^{2} (2 x) (2 \sec^{2} (2 x)))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.7.1.14.1.6

Reescribe con la propiedad conmutativa de la multiplicación.

$\frac{4 \sec^{4} (2 x) + 12 \sec^{3} (2 x) \tan (2 x) + 12 \sec^{2} (2 x) \tan^{2} (2 x) + 4 \tan^{3} (2 x) \sec (2 x) + 2 (- 2 \sec^{2} (2 x) \tan^{2} (2 x) - 2 \sec^{3} (2 x) \tan (2 x) - 2 \sec^{3} (2 x) \tan (2 x) - 1 \cdot 2 \sec^{2} (2 x) \sec^{2} (2 x))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.7.1.14.1.7

Multiplica $\sec^{2} (2 x)$ por $\sec^{2} (2 x)$ sumando los exponentes.

Toca para ver más pasos...

Paso 2.15.7.1.14.1.7.1

Mueve $\sec^{2} (2 x)$ .

$\frac{4 \sec^{4} (2 x) + 12 \sec^{3} (2 x) \tan (2 x) + 12 \sec^{2} (2 x) \tan^{2} (2 x) + 4 \tan^{3} (2 x) \sec (2 x) + 2 (- 2 \sec^{2} (2 x) \tan^{2} (2 x) - 2 \sec^{3} (2 x) \tan (2 x) - 2 \sec^{3} (2 x) \tan (2 x) - 1 \cdot 2 (\sec^{2} (2 x) \sec^{2} (2 x)))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.7.1.14.1.7.2

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

$\frac{4 \sec^{4} (2 x) + 12 \sec^{3} (2 x) \tan (2 x) + 12 \sec^{2} (2 x) \tan^{2} (2 x) + 4 \tan^{3} (2 x) \sec (2 x) + 2 (- 2 \sec^{2} (2 x) \tan^{2} (2 x) - 2 \sec^{3} (2 x) \tan (2 x) - 2 \sec^{3} (2 x) \tan (2 x) - 1 \cdot 2 {\sec (2 x)}^{2 + 2})}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.7.1.14.1.7.3

Suma $2$ y $2$ .

$\frac{4 \sec^{4} (2 x) + 12 \sec^{3} (2 x) \tan (2 x) + 12 \sec^{2} (2 x) \tan^{2} (2 x) + 4 \tan^{3} (2 x) \sec (2 x) + 2 (- 2 \sec^{2} (2 x) \tan^{2} (2 x) - 2 \sec^{3} (2 x) \tan (2 x) - 2 \sec^{3} (2 x) \tan (2 x) - 1 \cdot 2 \sec^{4} (2 x))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.7.1.14.1.8

Multiplica $- 1$ por $2$ .

$\frac{4 \sec^{4} (2 x) + 12 \sec^{3} (2 x) \tan (2 x) + 12 \sec^{2} (2 x) \tan^{2} (2 x) + 4 \tan^{3} (2 x) \sec (2 x) + 2 (- 2 \sec^{2} (2 x) \tan^{2} (2 x) - 2 \sec^{3} (2 x) \tan (2 x) - 2 \sec^{3} (2 x) \tan (2 x) - 2 \sec^{4} (2 x))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.7.1.14.2

Resta $2 \sec^{3} (2 x) \tan (2 x)$ de $- 2 \sec^{3} (2 x) \tan (2 x)$ .

$\frac{4 \sec^{4} (2 x) + 12 \sec^{3} (2 x) \tan (2 x) + 12 \sec^{2} (2 x) \tan^{2} (2 x) + 4 \tan^{3} (2 x) \sec (2 x) + 2 (- 2 \sec^{2} (2 x) \tan^{2} (2 x) - 4 \sec^{3} (2 x) \tan (2 x) - 2 \sec^{4} (2 x))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.7.1.15

Aplica la propiedad distributiva.

$\frac{4 \sec^{4} (2 x) + 12 \sec^{3} (2 x) \tan (2 x) + 12 \sec^{2} (2 x) \tan^{2} (2 x) + 4 \tan^{3} (2 x) \sec (2 x) + 2 (- 2 \sec^{2} (2 x) \tan^{2} (2 x)) + 2 (- 4 \sec^{3} (2 x) \tan (2 x)) + 2 (- 2 \sec^{4} (2 x))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.7.1.16

Simplifica.

Toca para ver más pasos...

Paso 2.15.7.1.16.1

Multiplica $- 2$ por $2$ .

$\frac{4 \sec^{4} (2 x) + 12 \sec^{3} (2 x) \tan (2 x) + 12 \sec^{2} (2 x) \tan^{2} (2 x) + 4 \tan^{3} (2 x) \sec (2 x) - 4 (\sec^{2} (2 x) \tan^{2} (2 x)) + 2 (- 4 \sec^{3} (2 x) \tan (2 x)) + 2 (- 2 \sec^{4} (2 x))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.7.1.16.2

Multiplica $- 4$ por $2$ .

$\frac{4 \sec^{4} (2 x) + 12 \sec^{3} (2 x) \tan (2 x) + 12 \sec^{2} (2 x) \tan^{2} (2 x) + 4 \tan^{3} (2 x) \sec (2 x) - 4 (\sec^{2} (2 x) \tan^{2} (2 x)) - 8 (\sec^{3} (2 x) \tan (2 x)) + 2 (- 2 \sec^{4} (2 x))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.7.1.16.3

Multiplica $- 2$ por $2$ .

$\frac{4 \sec^{4} (2 x) + 12 \sec^{3} (2 x) \tan (2 x) + 12 \sec^{2} (2 x) \tan^{2} (2 x) + 4 \tan^{3} (2 x) \sec (2 x) - 4 (\sec^{2} (2 x) \tan^{2} (2 x)) - 8 (\sec^{3} (2 x) \tan (2 x)) - 4 \sec^{4} (2 x)}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.7.1.17

Elimina los paréntesis.

$\frac{4 \sec^{4} (2 x) + 12 \sec^{3} (2 x) \tan (2 x) + 12 \sec^{2} (2 x) \tan^{2} (2 x) + 4 \tan^{3} (2 x) \sec (2 x) - 4 \sec^{2} (2 x) \tan^{2} (2 x) - 8 \sec^{3} (2 x) \tan (2 x) - 4 \sec^{4} (2 x)}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.7.2

Combina los términos opuestos en $4 \sec^{4} (2 x) + 12 \sec^{3} (2 x) \tan (2 x) + 12 \sec^{2} (2 x) \tan^{2} (2 x) + 4 \tan^{3} (2 x) \sec (2 x) - 4 \sec^{2} (2 x) \tan^{2} (2 x) - 8 \sec^{3} (2 x) \tan (2 x) - 4 \sec^{4} (2 x)$ .

Toca para ver más pasos...

Paso 2.15.7.2.1

Resta $4 \sec^{4} (2 x)$ de $4 \sec^{4} (2 x)$ .

$\frac{12 \sec^{3} (2 x) \tan (2 x) + 12 \sec^{2} (2 x) \tan^{2} (2 x) + 4 \tan^{3} (2 x) \sec (2 x) - 4 \sec^{2} (2 x) \tan^{2} (2 x) - 8 \sec^{3} (2 x) \tan (2 x) + 0}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.7.2.2

Suma $12 \sec^{3} (2 x) \tan (2 x) + 12 \sec^{2} (2 x) \tan^{2} (2 x) + 4 \tan^{3} (2 x) \sec (2 x) - 4 \sec^{2} (2 x) \tan^{2} (2 x) - 8 \sec^{3} (2 x) \tan (2 x)$ y $0$ .

$\frac{12 \sec^{3} (2 x) \tan (2 x) + 12 \sec^{2} (2 x) \tan^{2} (2 x) + 4 \tan^{3} (2 x) \sec (2 x) - 4 \sec^{2} (2 x) \tan^{2} (2 x) - 8 \sec^{3} (2 x) \tan (2 x)}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.7.3

Resta $8 \sec^{3} (2 x) \tan (2 x)$ de $12 \sec^{3} (2 x) \tan (2 x)$ .

$\frac{4 \sec^{3} (2 x) \tan (2 x) + 12 \sec^{2} (2 x) \tan^{2} (2 x) + 4 \tan^{3} (2 x) \sec (2 x) - 4 \sec^{2} (2 x) \tan^{2} (2 x)}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.7.4

Resta $4 \sec^{2} (2 x) \tan^{2} (2 x)$ de $12 \sec^{2} (2 x) \tan^{2} (2 x)$ .

$\frac{4 \sec^{3} (2 x) \tan (2 x) + 8 \sec^{2} (2 x) \tan^{2} (2 x) + 4 \tan^{3} (2 x) \sec (2 x)}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.8

Simplifica el numerador.

Toca para ver más pasos...

Paso 2.15.8.1

Factoriza $4 \sec (2 x) \tan (2 x)$ de $4 \sec^{3} (2 x) \tan (2 x) + 8 \sec^{2} (2 x) \tan^{2} (2 x) + 4 \tan^{3} (2 x) \sec (2 x)$ .

Toca para ver más pasos...

Paso 2.15.8.1.1

Factoriza $4 \sec (2 x) \tan (2 x)$ de $4 \sec^{3} (2 x) \tan (2 x)$ .

$\frac{4 \sec (2 x) \tan (2 x) (\sec^{2} (2 x)) + 8 \sec^{2} (2 x) \tan^{2} (2 x) + 4 \tan^{3} (2 x) \sec (2 x)}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.8.1.2

Factoriza $4 \sec (2 x) \tan (2 x)$ de $8 \sec^{2} (2 x) \tan^{2} (2 x)$ .

$\frac{4 \sec (2 x) \tan (2 x) (\sec^{2} (2 x)) + 4 \sec (2 x) \tan (2 x) (2 \sec (2 x) \tan (2 x)) + 4 \tan^{3} (2 x) \sec (2 x)}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.8.1.3

Factoriza $4 \sec (2 x) \tan (2 x)$ de $4 \tan^{3} (2 x) \sec (2 x)$ .

$\frac{4 \sec (2 x) \tan (2 x) (\sec^{2} (2 x)) + 4 \sec (2 x) \tan (2 x) (2 \sec (2 x) \tan (2 x)) + 4 \sec (2 x) \tan (2 x) (\tan^{2} (2 x))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.8.1.4

Factoriza $4 \sec (2 x) \tan (2 x)$ de $4 \sec (2 x) \tan (2 x) (\sec^{2} (2 x)) + 4 \sec (2 x) \tan (2 x) (2 \sec (2 x) \tan (2 x))$ .

$\frac{4 \sec (2 x) \tan (2 x) (\sec^{2} (2 x) + 2 \sec (2 x) \tan (2 x)) + 4 \sec (2 x) \tan (2 x) (\tan^{2} (2 x))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.8.1.5

Factoriza $4 \sec (2 x) \tan (2 x)$ de $4 \sec (2 x) \tan (2 x) (\sec^{2} (2 x) + 2 \sec (2 x) \tan (2 x)) + 4 \sec (2 x) \tan (2 x) (\tan^{2} (2 x))$ .

$\frac{4 \sec (2 x) \tan (2 x) (\sec^{2} (2 x) + 2 \sec (2 x) \tan (2 x) + \tan^{2} (2 x))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.8.2

Factoriza con la regla del cuadrado perfecto.

Toca para ver más pasos...

Paso 2.15.8.2.1

Comprueba que el término medio sea dos veces el producto de los números que se elevan al cuadrado en el primer término y el tercer término.

$2 \sec (2 x) \tan (2 x) = 2 \cdot \sec (2 x) \cdot \tan (2 x)$

Paso 2.15.8.2.2

Reescribe el polinomio.

$\frac{4 \sec (2 x) \tan (2 x) (\sec^{2} (2 x) + 2 \cdot \sec (2 x) \cdot \tan (2 x) + \tan^{2} (2 x))}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.8.2.3

Factoriza con la regla del trinomio cuadrado perfecto $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , donde $a = \sec (2 x)$ y $b = \tan (2 x)$ .

$\frac{4 \sec (2 x) \tan (2 x) {(\sec (2 x) + \tan (2 x))}^{2}}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.9

Cancela el factor común de ${(\sec (2 x) + \tan (2 x))}^{2}$ .

Toca para ver más pasos...

Paso 2.15.9.1

Cancela el factor común.

$\frac{4 \sec (2 x) \tan (2 x) {(\sec (2 x) + \tan (2 x))}^{2}}{{(\sec (2 x) + \tan (2 x))}^{2}}$

Paso 2.15.9.2

Divide $4 \sec (2 x) \tan (2 x)$ por $1$ .

$f'' (x) = 4 \sec (2 x) \tan (2 x)$