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

Derivative of sin(t)^(3)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   3   
sin (t)
$$\sin^{3}{\left(t \right)}$$ 
d /   3   \
--\sin (t)/
dt
$$\frac{d}{d t} \sin^{3}{\left(t \right)}$$
Transform
Detail solution

  1. Let .

  2. Apply the power rule: goes to

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

    1. The derivative of sine is cosine:

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