Derivative of cos^5x

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   5   
cos (x)

$$\cos^{5}{\left(x \right)}$$

d /   5   \
--\cos (x)/
dx

$$\frac{d}{d x} \cos^{5}{\left(x \right)}$$

Transform

Detail solution

The answer is:

$- 5 \sin{\left(x \right)} \cos^{4}{\left(x \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

      4          
-5*cos (x)*sin(x)

$$- 5 \sin{\left(x \right)} \cos^{4}{\left(x \right)}$$

Simplify

The second derivative [src]

     3    /     2           2   \
5*cos (x)*\- cos (x) + 4*sin (x)/

$$5 \cdot \left(4 \sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right) \cos^{3}{\left(x \right)}$$

Simplify

The third derivative [src]

     2    /        2            2   \       
5*cos (x)*\- 12*sin (x) + 13*cos (x)/*sin(x)

$$5 \left(- 12 \sin^{2}{\left(x \right)} + 13 \cos^{2}{\left(x \right)}\right) \sin{\left(x \right)} \cos^{2}{\left(x \right)}$$

Simplify

The graph