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cos^3x
The derivative of the function/ cos^3x

Derivative of cos^3x

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   3   
cos (x)
$$\cos^{3}{\left(x \right)}$$ 
d /   3   \
--\cos (x)/
dx
$$\frac{d}{d x} \cos^{3}{\left(x \right)}$$
Transform
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:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
      2          
-3*cos (x)*sin(x)
$$- 3 \sin{\left(x \right)} \cos^{2}{\left(x \right)}$$
Simplify
The second derivative [src] 
  /     2           2   \       
3*\- cos (x) + 2*sin (x)/*cos(x)
$$3 \cdot \left(2 \sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right) \cos{\left(x \right)}$$
Simplify
The third derivative [src] 
  /       2           2   \       
3*\- 2*sin (x) + 7*cos (x)/*sin(x)
$$3 \left(- 2 \sin^{2}{\left(x \right)} + 7 \cos^{2}{\left(x \right)}\right) \sin{\left(x \right)}$$
Simplify
The graph
Derivative of cos^3x
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