Mister Exam

Derivative of sin^5x

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
   5   
sin (x)
$$\sin^{5}{\left(x \right)}$$
d /   5   \
--\sin (x)/
dx         
$$\frac{d}{d x} \sin^{5}{\left(x \right)}$$
Detail solution
  1. Let .

  2. Apply the power rule: goes to

  3. Then, apply the chain rule. Multiply by :

    1. The derivative of sine is cosine:

    The result of the chain rule is:


The answer is:

The graph
The first derivative [src]
     4          
5*sin (x)*cos(x)
$$5 \sin^{4}{\left(x \right)} \cos{\left(x \right)}$$
The second derivative [src]
     3    /     2           2   \
5*sin (x)*\- sin (x) + 4*cos (x)/
$$5 \left(- \sin^{2}{\left(x \right)} + 4 \cos^{2}{\left(x \right)}\right) \sin^{3}{\left(x \right)}$$
The third derivative [src]
     2    /        2            2   \       
5*sin (x)*\- 13*sin (x) + 12*cos (x)/*cos(x)
$$5 \left(- 13 \sin^{2}{\left(x \right)} + 12 \cos^{2}{\left(x \right)}\right) \sin^{2}{\left(x \right)} \cos{\left(x \right)}$$
The graph
Derivative of sin^5x