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cos^3x^2

Derivative of cos^3x^2

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
        / 2\
        \3 /
(cos(x))    
$$\cos^{3^{2}}{\left(x \right)}$$
  /        / 2\\
d |        \3 /|
--\(cos(x))    /
dx              
$$\frac{d}{d x} \cos^{3^{2}}{\left(x \right)}$$
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:

  4. Now simplify:


The answer is:

The graph
The first derivative [src]
           / 2\       
           \3 /       
-9*(cos(x))    *sin(x)
----------------------
        cos(x)        
$$- \frac{9 \sin{\left(x \right)} \cos^{3^{2}}{\left(x \right)}}{\cos{\left(x \right)}}$$
The second derivative [src]
     7    /     2           2   \
9*cos (x)*\- cos (x) + 8*sin (x)/
$$9 \cdot \left(8 \sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right) \cos^{7}{\left(x \right)}$$
The third derivative [src]
     6    /        2            2   \       
9*cos (x)*\- 56*sin (x) + 25*cos (x)/*sin(x)
$$9 \left(- 56 \sin^{2}{\left(x \right)} + 25 \cos^{2}{\left(x \right)}\right) \sin{\left(x \right)} \cos^{6}{\left(x \right)}$$
The graph
Derivative of cos^3x^2