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The derivative of the function/ sin(x)^10

Derivative of sin(x)^10

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   10   
sin  (x)
$$\sin^{10}{\left(x \right)}$$ 
sin(x)^10
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] 
      9          
10*sin (x)*cos(x)
$$10 \sin^{9}{\left(x \right)} \cos{\left(x \right)}$$
Simplify
The second derivative [src] 
      8    /     2           2   \
10*sin (x)*\- sin (x) + 9*cos (x)/
$$10 \left(- \sin^{2}{\left(x \right)} + 9 \cos^{2}{\left(x \right)}\right) \sin^{8}{\left(x \right)}$$
Simplify
The third derivative [src] 
      7    /       2            2   \       
40*sin (x)*\- 7*sin (x) + 18*cos (x)/*cos(x)
$$40 \left(- 7 \sin^{2}{\left(x \right)} + 18 \cos^{2}{\left(x \right)}\right) \sin^{7}{\left(x \right)} \cos{\left(x \right)}$$
Simplify
4-я производная [src] 
      6    /     4             4             2       2   \
40*sin (x)*\7*sin (x) + 126*cos (x) - 117*cos (x)*sin (x)/
$$40 \left(7 \sin^{4}{\left(x \right)} - 117 \sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)} + 126 \cos^{4}{\left(x \right)}\right) \sin^{6}{\left(x \right)}$$
Simplify
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