Mister Exam

Derivative of cos2x^2

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
   2     
cos (2*x)
$$\cos^{2}{\left(2 x \right)}$$
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 cosine is negative sine:

    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*\sin (2*x) - cos (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 cos2x^2