Derivative of arctg5^x

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    x   
atan (5)

$$\operatorname{atan}^{x}{\left(5 \right)}$$

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Detail solution

$\frac{d}{d x} \operatorname{atan}^{x}{\left(5 \right)} = \log{\left(\operatorname{atan}{\left(5 \right)} \right)} \operatorname{atan}^{x}{\left(5 \right)}$

The answer is:

$\log{\left(\operatorname{atan}{\left(5 \right)} \right)} \operatorname{atan}^{x}{\left(5 \right)}$

The graph

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The first derivative [src]

    x                
atan (5)*log(atan(5))

$$\log{\left(\operatorname{atan}{\left(5 \right)} \right)} \operatorname{atan}^{x}{\left(5 \right)}$$

Simplify

The second derivative [src]

    x       2         
atan (5)*log (atan(5))

$$\log{\left(\operatorname{atan}{\left(5 \right)} \right)}^{2} \operatorname{atan}^{x}{\left(5 \right)}$$

Simplify

The third derivative [src]

    x       3         
atan (5)*log (atan(5))

$$\log{\left(\operatorname{atan}{\left(5 \right)} \right)}^{3} \operatorname{atan}^{x}{\left(5 \right)}$$

Simplify

The graph