Derivative of sin⁹x

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   9   
sin (x)

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

d /   9   \
--\sin (x)/
dx

$$\frac{d}{d x} \sin^{9}{\left(x \right)}$$

Transform

Detail solution

The answer is:

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

The graph

Plot the graph f(x)

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The first derivative [src]

     8          
9*sin (x)*cos(x)

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

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