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cos^34x
The derivative of the function/ cos^34x

Derivative of cos^34x

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   34   
cos  (x)
$$\cos^{34}{\left(x \right)}$$
Transform
Detail solution

  1. Let .

  2. Apply the power rule: goes to

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

    1. The derivative of 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] 
       33          
-34*cos  (x)*sin(x)
$$- 34 \sin{\left(x \right)} \cos^{33}{\left(x \right)}$$
Simplify
The second derivative [src] 
      32    /     2            2   \
34*cos  (x)*\- cos (x) + 33*sin (x)/
$$34 \left(33 \sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right) \cos^{32}{\left(x \right)}$$
Simplify
The third derivative [src] 
       31    /         2            2   \       
136*cos  (x)*\- 264*sin (x) + 25*cos (x)/*sin(x)
$$136 \left(- 264 \sin^{2}{\left(x \right)} + 25 \cos^{2}{\left(x \right)}\right) \sin{\left(x \right)} \cos^{31}{\left(x \right)}$$
Simplify
The graph
Derivative of cos^34x
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