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The derivative of the function/ cosx^sin2x

Derivative of cosx^sin2x

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   sin(2*x)   
cos        (x)
$$\cos^{\sin{\left(2 x \right)}}{\left(x \right)}$$ 
cos(x)^sin(2*x)
Detail solution

  1. Don't know the steps in finding this derivative.

    But the derivative is

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
   sin(2*x)    /                         sin(x)*sin(2*x)\
cos        (x)*|2*cos(2*x)*log(cos(x)) - ---------------|
               \                              cos(x)    /
$$\left(2 \log{\left(\cos{\left(x \right)} \right)} \cos{\left(2 x \right)} - \frac{\sin{\left(x \right)} \sin{\left(2 x \right)}}{\cos{\left(x \right)}}\right) \cos^{\sin{\left(2 x \right)}}{\left(x \right)}$$
Simplify
The second derivative [src] 
               /                                          2                                          2                                \
   sin(2*x)    |/                         sin(x)*sin(2*x)\                                        sin (x)*sin(2*x)   4*cos(2*x)*sin(x)|
cos        (x)*||2*cos(2*x)*log(cos(x)) - ---------------|  - sin(2*x) - 4*log(cos(x))*sin(2*x) - ---------------- - -----------------|
               |\                              cos(x)    /                                               2                 cos(x)     |
               \                                                                                      cos (x)                         /
$$\left(\left(2 \log{\left(\cos{\left(x \right)} \right)} \cos{\left(2 x \right)} - \frac{\sin{\left(x \right)} \sin{\left(2 x \right)}}{\cos{\left(x \right)}}\right)^{2} - 4 \log{\left(\cos{\left(x \right)} \right)} \sin{\left(2 x \right)} - \frac{\sin^{2}{\left(x \right)} \sin{\left(2 x \right)}}{\cos^{2}{\left(x \right)}} - \frac{4 \sin{\left(x \right)} \cos{\left(2 x \right)}}{\cos{\left(x \right)}} - \sin{\left(2 x \right)}\right) \cos^{\sin{\left(2 x \right)}}{\left(x \right)}$$
Simplify
The third derivative [src] 
               /                                          3                                                                                      /                            2                                           \        2                    3                                 \
   sin(2*x)    |/                         sin(x)*sin(2*x)\                                            /                         sin(x)*sin(2*x)\ |                         sin (x)*sin(2*x)   4*cos(2*x)*sin(x)           |   6*sin (x)*cos(2*x)   2*sin (x)*sin(2*x)   10*sin(x)*sin(2*x)|
cos        (x)*||2*cos(2*x)*log(cos(x)) - ---------------|  - 6*cos(2*x) - 8*cos(2*x)*log(cos(x)) - 3*|2*cos(2*x)*log(cos(x)) - ---------------|*|4*log(cos(x))*sin(2*x) + ---------------- + ----------------- + sin(2*x)| - ------------------ - ------------------ + ------------------|
               |\                              cos(x)    /                                            \                              cos(x)    / |                                2                 cos(x)                |           2                    3                  cos(x)      |
               \                                                                                                                                 \                             cos (x)                                    /        cos (x)              cos (x)                           /
$$\left(\left(2 \log{\left(\cos{\left(x \right)} \right)} \cos{\left(2 x \right)} - \frac{\sin{\left(x \right)} \sin{\left(2 x \right)}}{\cos{\left(x \right)}}\right)^{3} - 3 \left(2 \log{\left(\cos{\left(x \right)} \right)} \cos{\left(2 x \right)} - \frac{\sin{\left(x \right)} \sin{\left(2 x \right)}}{\cos{\left(x \right)}}\right) \left(4 \log{\left(\cos{\left(x \right)} \right)} \sin{\left(2 x \right)} + \frac{\sin^{2}{\left(x \right)} \sin{\left(2 x \right)}}{\cos^{2}{\left(x \right)}} + \frac{4 \sin{\left(x \right)} \cos{\left(2 x \right)}}{\cos{\left(x \right)}} + \sin{\left(2 x \right)}\right) - 8 \log{\left(\cos{\left(x \right)} \right)} \cos{\left(2 x \right)} - \frac{2 \sin^{3}{\left(x \right)} \sin{\left(2 x \right)}}{\cos^{3}{\left(x \right)}} - \frac{6 \sin^{2}{\left(x \right)} \cos{\left(2 x \right)}}{\cos^{2}{\left(x \right)}} + \frac{10 \sin{\left(x \right)} \sin{\left(2 x \right)}}{\cos{\left(x \right)}} - 6 \cos{\left(2 x \right)}\right) \cos^{\sin{\left(2 x \right)}}{\left(x \right)}$$
Simplify
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