Mister Exam

Other calculators

sin^23x
The derivative of the function/ sin^23x

Derivative of sin^23x

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   23   
sin  (x)
$$\sin^{23}{\left(x \right)}$$ 
sin(x)^23
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
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
      22          
23*sin  (x)*cos(x)
$$23 \sin^{22}{\left(x \right)} \cos{\left(x \right)}$$
Simplify
The second derivative [src] 
      21    /     2            2   \
23*sin  (x)*\- sin (x) + 22*cos (x)/
$$23 \left(- \sin^{2}{\left(x \right)} + 22 \cos^{2}{\left(x \right)}\right) \sin^{21}{\left(x \right)}$$
Simplify
The third derivative [src] 
      20    /        2             2   \       
23*sin  (x)*\- 67*sin (x) + 462*cos (x)/*cos(x)
$$23 \left(- 67 \sin^{2}{\left(x \right)} + 462 \cos^{2}{\left(x \right)}\right) \sin^{20}{\left(x \right)} \cos{\left(x \right)}$$
Simplify
The graph
Derivative of sin^23x
    © Mister Exam – Calculator