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cos^3(t)
The derivative of the function/ cos^3(t)

Derivative of cos^3(t)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   3   
cos (t)
$$\cos^{3}{\left(t \right)}$$ 
d /   3   \
--\cos (t)/
dt
$$\frac{d}{d t} \cos^{3}{\left(t \right)}$$
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 (t)*sin(t)
$$- 3 \sin{\left(t \right)} \cos^{2}{\left(t \right)}$$
Simplify
The second derivative [src] 
  /     2           2   \       
3*\- cos (t) + 2*sin (t)/*cos(t)
$$3 \cdot \left(2 \sin^{2}{\left(t \right)} - \cos^{2}{\left(t \right)}\right) \cos{\left(t \right)}$$
Simplify
The third derivative [src] 
  /       2           2   \       
3*\- 2*sin (t) + 7*cos (t)/*sin(t)
$$3 \left(- 2 \sin^{2}{\left(t \right)} + 7 \cos^{2}{\left(t \right)}\right) \sin{\left(t \right)}$$
Simplify
The graph
Derivative of cos^3(t)
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