Mister Exam

Derivative of sin(3x)^4

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
   4     
sin (3*x)
$$\sin^{4}{\left(3 x \right)}$$
sin(3*x)^4
Detail solution
  1. Let .

  2. Apply the power rule: goes to

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

    1. Let .

    2. The derivative of sine is cosine:

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

      1. The derivative of a constant times a function is the constant times the derivative of the function.

        1. Apply the power rule: goes to

        So, the result is:

      The result of the chain rule is:

    The result of the chain rule is:


The answer is:

The graph
The first derivative [src]
      3              
12*sin (3*x)*cos(3*x)
$$12 \sin^{3}{\left(3 x \right)} \cos{\left(3 x \right)}$$
The second derivative [src]
      2      /     2             2     \
36*sin (3*x)*\- sin (3*x) + 3*cos (3*x)/
$$36 \left(- \sin^{2}{\left(3 x \right)} + 3 \cos^{2}{\left(3 x \right)}\right) \sin^{2}{\left(3 x \right)}$$
The third derivative [src]
    /       2             2     \                  
216*\- 5*sin (3*x) + 3*cos (3*x)/*cos(3*x)*sin(3*x)
$$216 \left(- 5 \sin^{2}{\left(3 x \right)} + 3 \cos^{2}{\left(3 x \right)}\right) \sin{\left(3 x \right)} \cos{\left(3 x \right)}$$