Derivative of sin³x²

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        / 2\
        \3 /
(sin(x))

$$\sin^{3^{2}}{\left(x \right)}$$

  /        / 2\\
d |        \3 /|
--\(sin(x))    /
dx

$$\frac{d}{d x} \sin^{3^{2}}{\left(x \right)}$$

Transform

Detail solution

The answer is:

$9 \sin^{8}{\left(x \right)} \cos{\left(x \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

          / 2\       
          \3 /       
9*(sin(x))    *cos(x)
---------------------
        sin(x)

$$\frac{9 \sin^{3^{2}}{\left(x \right)} \cos{\left(x \right)}}{\sin{\left(x \right)}}$$

Simplify

The second derivative [src]

     7    /     2           2   \
9*sin (x)*\- sin (x) + 8*cos (x)/

$$9 \left(- \sin^{2}{\left(x \right)} + 8 \cos^{2}{\left(x \right)}\right) \sin^{7}{\left(x \right)}$$

Simplify

The third derivative [src]

     6    /        2            2   \       
9*sin (x)*\- 25*sin (x) + 56*cos (x)/*cos(x)

$$9 \left(- 25 \sin^{2}{\left(x \right)} + 56 \cos^{2}{\left(x \right)}\right) \sin^{6}{\left(x \right)} \cos{\left(x \right)}$$

Simplify

The graph