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cos^2(5x)

Derivative of cos^2(5x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
   2     
cos (5*x)
$$\cos^{2}{\left(5 x \right)}$$
cos(5*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 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]
-10*cos(5*x)*sin(5*x)
$$- 10 \sin{\left(5 x \right)} \cos{\left(5 x \right)}$$
The second derivative [src]
   /   2           2     \
50*\sin (5*x) - cos (5*x)/
$$50 \left(\sin^{2}{\left(5 x \right)} - \cos^{2}{\left(5 x \right)}\right)$$
The third derivative [src]
1000*cos(5*x)*sin(5*x)
$$1000 \sin{\left(5 x \right)} \cos{\left(5 x \right)}$$
The graph
Derivative of cos^2(5x)