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sin^5*x
The derivative of the function/ sin^5*x

Derivative of sin^5*x

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   5   
sin (x)
$$\sin^{5}{\left(x \right)}$$ 
sin(x)^5
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] 
     4          
5*sin (x)*cos(x)
$$5 \sin^{4}{\left(x \right)} \cos{\left(x \right)}$$
Simplify
The second derivative [src] 
     3    /     2           2   \
5*sin (x)*\- sin (x) + 4*cos (x)/
$$5 \left(- \sin^{2}{\left(x \right)} + 4 \cos^{2}{\left(x \right)}\right) \sin^{3}{\left(x \right)}$$
Simplify
The third derivative [src] 
     2    /        2            2   \       
5*sin (x)*\- 13*sin (x) + 12*cos (x)/*cos(x)
$$5 \left(- 13 \sin^{2}{\left(x \right)} + 12 \cos^{2}{\left(x \right)}\right) \sin^{2}{\left(x \right)} \cos{\left(x \right)}$$
Simplify
The graph
Derivative of sin^5*x
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