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sin^2(2x)

Derivative of sin^2(2x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
   2     
sin (2*x)
$$\sin^{2}{\left(2 x \right)}$$
sin(2*x)^2
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:

  4. Now simplify:


The answer is:

The graph
The first derivative [src]
4*cos(2*x)*sin(2*x)
$$4 \sin{\left(2 x \right)} \cos{\left(2 x \right)}$$
The second derivative [src]
  /   2           2     \
8*\cos (2*x) - sin (2*x)/
$$8 \left(- \sin^{2}{\left(2 x \right)} + \cos^{2}{\left(2 x \right)}\right)$$
The third derivative [src]
-64*cos(2*x)*sin(2*x)
$$- 64 \sin{\left(2 x \right)} \cos{\left(2 x \right)}$$
The graph
Derivative of sin^2(2x)