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sin²5x
The derivative of the function/ sin²5x

Derivative of sin²5x

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   25   
sin  (x)
$$\sin^{25}{\left(x \right)}$$ 
d /   25   \
--\sin  (x)/
dx
$$\frac{d}{d x} \sin^{25}{\left(x \right)}$$
Transform
Detail solution

  1. Let .

  2. Apply the power rule: goes to

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

    1. The derivative of sine is cosine:

    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] 
      24          
25*sin  (x)*cos(x)
$$25 \sin^{24}{\left(x \right)} \cos{\left(x \right)}$$
Simplify
The second derivative [src] 
      23    /     2            2   \
25*sin  (x)*\- sin (x) + 24*cos (x)/
$$25 \left(- \sin^{2}{\left(x \right)} + 24 \cos^{2}{\left(x \right)}\right) \sin^{23}{\left(x \right)}$$
Simplify
The third derivative [src] 
      22    /        2             2   \       
25*sin  (x)*\- 73*sin (x) + 552*cos (x)/*cos(x)
$$25 \left(- 73 \sin^{2}{\left(x \right)} + 552 \cos^{2}{\left(x \right)}\right) \sin^{22}{\left(x \right)} \cos{\left(x \right)}$$
Simplify
The graph
Derivative of sin²5x
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