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arctane^cosx
The derivative of the function/ arctane^cosx

Derivative of arctane^cosx

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
    cos(x)   
atan      (e)
$$\operatorname{atan}^{\cos{\left(x \right)}}{\left(e \right)}$$ 
d /    cos(x)   \
--\atan      (e)/
dx
$$\frac{d}{d x} \operatorname{atan}^{\cos{\left(x \right)}}{\left(e \right)}$$
Transform
Detail solution

  1. Let .

  3. Then, apply the chain rule. Multiply by :

    1. The derivative of cosine is negative sine:

    The result of the chain rule is:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
     cos(x)                       
-atan      (e)*log(atan(e))*sin(x)
$$- \log{\left(\operatorname{atan}{\left(e \right)} \right)} \sin{\left(x \right)} \operatorname{atan}^{\cos{\left(x \right)}}{\left(e \right)}$$
Simplify
The second derivative [src] 
    cos(x)    /             2                \             
atan      (e)*\-cos(x) + sin (x)*log(atan(e))/*log(atan(e))
$$\left(\log{\left(\operatorname{atan}{\left(e \right)} \right)} \sin^{2}{\left(x \right)} - \cos{\left(x \right)}\right) \log{\left(\operatorname{atan}{\left(e \right)} \right)} \operatorname{atan}^{\cos{\left(x \right)}}{\left(e \right)}$$
Simplify
The third derivative [src] 
    cos(x)    /       2             2                           \                    
atan      (e)*\1 - log (atan(e))*sin (x) + 3*cos(x)*log(atan(e))/*log(atan(e))*sin(x)
$$\left(- \log{\left(\operatorname{atan}{\left(e \right)} \right)}^{2} \sin^{2}{\left(x \right)} + 3 \log{\left(\operatorname{atan}{\left(e \right)} \right)} \cos{\left(x \right)} + 1\right) \log{\left(\operatorname{atan}{\left(e \right)} \right)} \sin{\left(x \right)} \operatorname{atan}^{\cos{\left(x \right)}}{\left(e \right)}$$
Simplify
The graph
Derivative of arctane^cosx
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