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cos^22t
The derivative of the function/ cos^22t

Derivative of cos^22t

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   22   
cos  (t)
$$\cos^{22}{\left(t \right)}$$ 
d /   22   \
--\cos  (t)/
dt
$$\frac{d}{d t} \cos^{22}{\left(t \right)}$$
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] 
       21          
-22*cos  (t)*sin(t)
$$- 22 \sin{\left(t \right)} \cos^{21}{\left(t \right)}$$
Simplify
The second derivative [src] 
      20    /     2            2   \
22*cos  (t)*\- cos (t) + 21*sin (t)/
$$22 \cdot \left(21 \sin^{2}{\left(t \right)} - \cos^{2}{\left(t \right)}\right) \cos^{20}{\left(t \right)}$$
Simplify
The third derivative [src] 
      19    /         2            2   \       
88*cos  (t)*\- 105*sin (t) + 16*cos (t)/*sin(t)
$$88 \left(- 105 \sin^{2}{\left(t \right)} + 16 \cos^{2}{\left(t \right)}\right) \sin{\left(t \right)} \cos^{19}{\left(t \right)}$$
Simplify
The graph
Derivative of cos^22t
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