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sin(2*x)^(3)

Derivative of sin(2*x)^(3)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
   3     
sin (2*x)
$$\sin^{3}{\left(2 x \right)}$$
sin(2*x)^3
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]
     2              
6*sin (2*x)*cos(2*x)
$$6 \sin^{2}{\left(2 x \right)} \cos{\left(2 x \right)}$$
The second derivative [src]
   /     2             2     \         
12*\- sin (2*x) + 2*cos (2*x)/*sin(2*x)
$$12 \left(- \sin^{2}{\left(2 x \right)} + 2 \cos^{2}{\left(2 x \right)}\right) \sin{\left(2 x \right)}$$
The third derivative [src]
   /       2             2     \         
24*\- 7*sin (2*x) + 2*cos (2*x)/*cos(2*x)
$$24 \left(- 7 \sin^{2}{\left(2 x \right)} + 2 \cos^{2}{\left(2 x \right)}\right) \cos{\left(2 x \right)}$$
The graph
Derivative of sin(2*x)^(3)