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y=sin20(x)
The derivative of the function/ y=sin20(x)

Derivative of y=sin20(x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   20   
sin  (x)
$$\sin^{20}{\left(x \right)}$$ 
sin(x)^20
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] 
      19          
20*sin  (x)*cos(x)
$$20 \sin^{19}{\left(x \right)} \cos{\left(x \right)}$$
Simplify
The second derivative [src] 
      18    /     2            2   \
20*sin  (x)*\- sin (x) + 19*cos (x)/
$$20 \left(- \sin^{2}{\left(x \right)} + 19 \cos^{2}{\left(x \right)}\right) \sin^{18}{\left(x \right)}$$
Simplify
The third derivative [src] 
      17    /        2             2   \       
40*sin  (x)*\- 29*sin (x) + 171*cos (x)/*cos(x)
$$40 \left(- 29 \sin^{2}{\left(x \right)} + 171 \cos^{2}{\left(x \right)}\right) \sin^{17}{\left(x \right)} \cos{\left(x \right)}$$
Simplify
The graph
Derivative of y=sin20(x)
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