Derivative of cos3^x

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   x   
cos (3)

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

cos(3)^x

Detail solution

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

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

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

Simplify

The graph