Derivada de cos3^x

Ha introducido [src]

   x   
cos (3)

$$\cos^{x}{\left(3 \right)}$$

cos(3)^x

Solución detallada

$\frac{d}{d x} \cos^{x}{\left(3 \right)} = \left(\log{\left(- \cos{\left(3 \right)} \right)} + i \pi\right) \cos^{x}{\left(3 \right)}$

Respuesta:

$\left(\log{\left(- \cos{\left(3 \right)} \right)} + i \pi\right) \cos^{x}{\left(3 \right)}$

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

   x                         
cos (3)*(pi*I + log(-cos(3)))

$$\left(\log{\left(- \cos{\left(3 \right)} \right)} + i \pi\right) \cos^{x}{\left(3 \right)}$$

Simplificar

Segunda derivada [src]

                     2    x   
(pi*I + log(-cos(3))) *cos (3)

$$\left(\log{\left(- \cos{\left(3 \right)} \right)} + i \pi\right)^{2} \cos^{x}{\left(3 \right)}$$

Simplificar

Tercera derivada [src]

                     3    x   
(pi*I + log(-cos(3))) *cos (3)

$$\left(\log{\left(- \cos{\left(3 \right)} \right)} + i \pi\right)^{3} \cos^{x}{\left(3 \right)}$$

Simplificar

Gráfico