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cos^7(x)
The derivative of the function/ cos^7(x)

Derivative of cos^7(x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   7   
cos (x)
$$\cos^{7}{\left(x \right)}$$ 
d /   7   \
--\cos (x)/
dx
$$\frac{d}{d x} \cos^{7}{\left(x \right)}$$
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] 
      6          
-7*cos (x)*sin(x)
$$- 7 \sin{\left(x \right)} \cos^{6}{\left(x \right)}$$
Simplify
The second derivative [src] 
     5    /     2           2   \
7*cos (x)*\- cos (x) + 6*sin (x)/
$$7 \cdot \left(6 \sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right) \cos^{5}{\left(x \right)}$$
Simplify
The third derivative [src] 
     4    /        2            2   \       
7*cos (x)*\- 30*sin (x) + 19*cos (x)/*sin(x)
$$7 \left(- 30 \sin^{2}{\left(x \right)} + 19 \cos^{2}{\left(x \right)}\right) \sin{\left(x \right)} \cos^{4}{\left(x \right)}$$
Simplify
The graph
Derivative of cos^7(x)
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