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Derivative of (sin(2x))^cos(3*x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
   cos(3*x)     
sin        (2*x)
$$\sin^{\cos{\left(3 x \right)}}{\left(2 x \right)}$$
sin(2*x)^cos(3*x)
Detail solution
  1. Don't know the steps in finding this derivative.

    But the derivative is


The answer is:

The graph
The first derivative [src]
   cos(3*x)      /                            2*cos(2*x)*cos(3*x)\
sin        (2*x)*|-3*log(sin(2*x))*sin(3*x) + -------------------|
                 \                                  sin(2*x)     /
$$\left(- 3 \log{\left(\sin{\left(2 x \right)} \right)} \sin{\left(3 x \right)} + \frac{2 \cos{\left(2 x \right)} \cos{\left(3 x \right)}}{\sin{\left(2 x \right)}}\right) \sin^{\cos{\left(3 x \right)}}{\left(2 x \right)}$$
The second derivative [src]
                 /                                                2                                                                       2              \
   cos(3*x)      |/                           2*cos(2*x)*cos(3*x)\                                            12*cos(2*x)*sin(3*x)   4*cos (2*x)*cos(3*x)|
sin        (2*x)*||3*log(sin(2*x))*sin(3*x) - -------------------|  - 4*cos(3*x) - 9*cos(3*x)*log(sin(2*x)) - -------------------- - --------------------|
                 |\                                 sin(2*x)     /                                                  sin(2*x)                 2           |
                 \                                                                                                                        sin (2*x)      /
$$\left(\left(3 \log{\left(\sin{\left(2 x \right)} \right)} \sin{\left(3 x \right)} - \frac{2 \cos{\left(2 x \right)} \cos{\left(3 x \right)}}{\sin{\left(2 x \right)}}\right)^{2} - 9 \log{\left(\sin{\left(2 x \right)} \right)} \cos{\left(3 x \right)} - 4 \cos{\left(3 x \right)} - \frac{12 \sin{\left(3 x \right)} \cos{\left(2 x \right)}}{\sin{\left(2 x \right)}} - \frac{4 \cos^{2}{\left(2 x \right)} \cos{\left(3 x \right)}}{\sin^{2}{\left(2 x \right)}}\right) \sin^{\cos{\left(3 x \right)}}{\left(2 x \right)}$$
The third derivative [src]
                 /                                                  3                                                                    /                                             2                                     \                                                            3                       2              \
   cos(3*x)      |  /                           2*cos(2*x)*cos(3*x)\                    /                           2*cos(2*x)*cos(3*x)\ |                                        4*cos (2*x)*cos(3*x)   12*cos(2*x)*sin(3*x)|                               38*cos(2*x)*cos(3*x)   16*cos (2*x)*cos(3*x)   36*cos (2*x)*sin(3*x)|
sin        (2*x)*|- |3*log(sin(2*x))*sin(3*x) - -------------------|  + 36*sin(3*x) + 3*|3*log(sin(2*x))*sin(3*x) - -------------------|*|4*cos(3*x) + 9*cos(3*x)*log(sin(2*x)) + -------------------- + --------------------| + 27*log(sin(2*x))*sin(3*x) - -------------------- + --------------------- + ---------------------|
                 |  \                                 sin(2*x)     /                    \                                 sin(2*x)     / |                                                2                    sin(2*x)      |                                     sin(2*x)                  3                       2           |
                 \                                                                                                                       \                                             sin (2*x)                             /                                                            sin (2*x)               sin (2*x)      /
$$\left(- \left(3 \log{\left(\sin{\left(2 x \right)} \right)} \sin{\left(3 x \right)} - \frac{2 \cos{\left(2 x \right)} \cos{\left(3 x \right)}}{\sin{\left(2 x \right)}}\right)^{3} + 3 \left(3 \log{\left(\sin{\left(2 x \right)} \right)} \sin{\left(3 x \right)} - \frac{2 \cos{\left(2 x \right)} \cos{\left(3 x \right)}}{\sin{\left(2 x \right)}}\right) \left(9 \log{\left(\sin{\left(2 x \right)} \right)} \cos{\left(3 x \right)} + 4 \cos{\left(3 x \right)} + \frac{12 \sin{\left(3 x \right)} \cos{\left(2 x \right)}}{\sin{\left(2 x \right)}} + \frac{4 \cos^{2}{\left(2 x \right)} \cos{\left(3 x \right)}}{\sin^{2}{\left(2 x \right)}}\right) + 27 \log{\left(\sin{\left(2 x \right)} \right)} \sin{\left(3 x \right)} + 36 \sin{\left(3 x \right)} - \frac{38 \cos{\left(2 x \right)} \cos{\left(3 x \right)}}{\sin{\left(2 x \right)}} + \frac{36 \sin{\left(3 x \right)} \cos^{2}{\left(2 x \right)}}{\sin^{2}{\left(2 x \right)}} + \frac{16 \cos^{3}{\left(2 x \right)} \cos{\left(3 x \right)}}{\sin^{3}{\left(2 x \right)}}\right) \sin^{\cos{\left(3 x \right)}}{\left(2 x \right)}$$