Mister Exam

Other calculators

cos^2x
The derivative of the function/ cos^2x

Derivative of cos^2x

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   2   
cos (x)
$$\cos^{2}{\left(x \right)}$$ 
cos(x)^2
Detail solution

  1. Let .

  2. Apply the power rule: goes to

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

    1. The derivative of cosine is negative sine:

    The result of the chain rule is:

  4. Now simplify:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
-2*cos(x)*sin(x)
$$- 2 \sin{\left(x \right)} \cos{\left(x \right)}$$
Simplify
The second derivative [src] 
  /   2         2   \
2*\sin (x) - cos (x)/
$$2 \left(\sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right)$$
Simplify
The third derivative [src] 
8*cos(x)*sin(x)
$$8 \sin{\left(x \right)} \cos{\left(x \right)}$$
Simplify
The graph
Derivative of cos^2x
    © Mister Exam – Calculator