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y=(sin2x)^cos2x
The derivative of the function/ y=(sin2x)^cos2x

Derivative of y=(sin2x)^cos2x

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

The graph:

from to

Piecewise:

The solution

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

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

    But the derivative is

    (log⁡(cos⁡(2x))+1)cos⁡cos⁡(2x)(2x)\left(\log{\left(\cos{\left(2 x \right)} \right)} + 1\right) \cos^{\cos{\left(2 x \right)}}{\left(2 x \right)}

The answer is:

(log⁡(cos⁡(2x))+1)cos⁡cos⁡(2x)(2x)\left(\log{\left(\cos{\left(2 x \right)} \right)} + 1\right) \cos^{\cos{\left(2 x \right)}}{\left(2 x \right)}

The graph
02468-8-6-4-2-10100500
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
                 /                                 2     \
   cos(2*x)      |                            2*cos (2*x)|
sin        (2*x)*|-2*log(sin(2*x))*sin(2*x) + -----------|
                 \                              sin(2*x) /
(−2log⁡(sin⁡(2x))sin⁡(2x)+2cos⁡2(2x)sin⁡(2x))sin⁡cos⁡(2x)(2x)\left(- 2 \log{\left(\sin{\left(2 x \right)} \right)} \sin{\left(2 x \right)} + \frac{2 \cos^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)}}\right) \sin^{\cos{\left(2 x \right)}}{\left(2 x \right)}
Simplify
The second derivative [src] 
                   /                                    2                                           \
                   |/                            2     \    /       2                     \         |
     cos(2*x)      ||                         cos (2*x)|    |    cos (2*x)                |         |
4*sin        (2*x)*||log(sin(2*x))*sin(2*x) - ---------|  - |3 + --------- + log(sin(2*x))|*cos(2*x)|
                   |\                          sin(2*x)/    |       2                     |         |
                   \                                        \    sin (2*x)                /         /
4((log⁡(sin⁡(2x))sin⁡(2x)−cos⁡2(2x)sin⁡(2x))2−(log⁡(sin⁡(2x))+3+cos⁡2(2x)sin⁡2(2x))cos⁡(2x))sin⁡cos⁡(2x)(2x)4 \left(\left(\log{\left(\sin{\left(2 x \right)} \right)} \sin{\left(2 x \right)} - \frac{\cos^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)}}\right)^{2} - \left(\log{\left(\sin{\left(2 x \right)} \right)} + 3 + \frac{\cos^{2}{\left(2 x \right)}}{\sin^{2}{\left(2 x \right)}}\right) \cos{\left(2 x \right)}\right) \sin^{\cos{\left(2 x \right)}}{\left(2 x \right)}
Simplify
The third derivative [src] 
                   /                                      3                                                                                                                                                    \
                   |  /                            2     \                                               2             4          /                            2     \ /       2                     \         |
     cos(2*x)      |  |                         cos (2*x)|                                          2*cos (2*x)   2*cos (2*x)     |                         cos (2*x)| |    cos (2*x)                |         |
8*sin        (2*x)*|- |log(sin(2*x))*sin(2*x) - ---------|  + 3*sin(2*x) + log(sin(2*x))*sin(2*x) + ----------- + ----------- + 3*|log(sin(2*x))*sin(2*x) - ---------|*|3 + --------- + log(sin(2*x))|*cos(2*x)|
                   |  \                          sin(2*x)/                                            sin(2*x)        3           \                          sin(2*x)/ |       2                     |         |
                   \                                                                                               sin (2*x)                                           \    sin (2*x)                /         /
8(−(log⁡(sin⁡(2x))sin⁡(2x)−cos⁡2(2x)sin⁡(2x))3+3(log⁡(sin⁡(2x))sin⁡(2x)−cos⁡2(2x)sin⁡(2x))(log⁡(sin⁡(2x))+3+cos⁡2(2x)sin⁡2(2x))cos⁡(2x)+log⁡(sin⁡(2x))sin⁡(2x)+3sin⁡(2x)+2cos⁡2(2x)sin⁡(2x)+2cos⁡4(2x)sin⁡3(2x))sin⁡cos⁡(2x)(2x)8 \left(- \left(\log{\left(\sin{\left(2 x \right)} \right)} \sin{\left(2 x \right)} - \frac{\cos^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)}}\right)^{3} + 3 \left(\log{\left(\sin{\left(2 x \right)} \right)} \sin{\left(2 x \right)} - \frac{\cos^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)}}\right) \left(\log{\left(\sin{\left(2 x \right)} \right)} + 3 + \frac{\cos^{2}{\left(2 x \right)}}{\sin^{2}{\left(2 x \right)}}\right) \cos{\left(2 x \right)} + \log{\left(\sin{\left(2 x \right)} \right)} \sin{\left(2 x \right)} + 3 \sin{\left(2 x \right)} + \frac{2 \cos^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)}} + \frac{2 \cos^{4}{\left(2 x \right)}}{\sin^{3}{\left(2 x \right)}}\right) \sin^{\cos{\left(2 x \right)}}{\left(2 x \right)}
Simplify
The graph
Derivative of y=(sin2x)^cos2x
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