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2*sin^5(x)
The derivative of the function/ 2*sin^5(x)

Derivative of 2*sin^5(x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
     5   
2*sin (x)
$$2 \sin^{5}{\left(x \right)}$$ 
d /     5   \
--\2*sin (x)/
dx
$$\frac{d}{d x} 2 \sin^{5}{\left(x \right)}$$
Transform
Detail solution

  1. The derivative of a constant times a function is the constant times the derivative of the function.

    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:

    So, the result is:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
      4          
10*sin (x)*cos(x)
$$10 \sin^{4}{\left(x \right)} \cos{\left(x \right)}$$
Simplify
The second derivative [src] 
       3    /   2           2   \
-10*sin (x)*\sin (x) - 4*cos (x)/
$$- 10 \left(\sin^{2}{\left(x \right)} - 4 \cos^{2}{\left(x \right)}\right) \sin^{3}{\left(x \right)}$$
Simplify
The third derivative [src] 
       2    /        2            2   \       
-10*sin (x)*\- 12*cos (x) + 13*sin (x)/*cos(x)
$$- 10 \cdot \left(13 \sin^{2}{\left(x \right)} - 12 \cos^{2}{\left(x \right)}\right) \sin^{2}{\left(x \right)} \cos{\left(x \right)}$$
Simplify
The graph
Derivative of 2*sin^5(x)
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