Derivative of y=sin⁶x

You have entered [src]

   6   
sin (x)

$$\sin^{6}{\left(x \right)}$$

d /   6   \
--\sin (x)/
dx

$$\frac{d}{d x} \sin^{6}{\left(x \right)}$$

Transform

Detail solution

The answer is:

$6 \sin^{5}{\left(x \right)} \cos{\left(x \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

     5          
6*sin (x)*cos(x)

$$6 \sin^{5}{\left(x \right)} \cos{\left(x \right)}$$

Simplify

The second derivative [src]

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

$$6 \left(- \sin^{2}{\left(x \right)} + 5 \cos^{2}{\left(x \right)}\right) \sin^{4}{\left(x \right)}$$

Simplify

The third derivative [src]

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

$$24 \left(- 4 \sin^{2}{\left(x \right)} + 5 \cos^{2}{\left(x \right)}\right) \sin^{3}{\left(x \right)} \cos{\left(x \right)}$$

Simplify

The graph