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The derivative of the function/ cos(x)^8

Derivative of cos(x)^8

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   8   
cos (x)
$$\cos^{8}{\left(x \right)}$$ 
cos(x)^8
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] 
      7          
-8*cos (x)*sin(x)
$$- 8 \sin{\left(x \right)} \cos^{7}{\left(x \right)}$$
Simplify
The second derivative [src] 
     6    /     2           2   \
8*cos (x)*\- cos (x) + 7*sin (x)/
$$8 \left(7 \sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right) \cos^{6}{\left(x \right)}$$
Simplify
The third derivative [src] 
      5    /        2            2   \       
16*cos (x)*\- 21*sin (x) + 11*cos (x)/*sin(x)
$$16 \left(- 21 \sin^{2}{\left(x \right)} + 11 \cos^{2}{\left(x \right)}\right) \sin{\left(x \right)} \cos^{5}{\left(x \right)}$$
Simplify
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