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  • Identical expressions

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  • Similar expressions

  • 8sin^2(x)*cosx

Derivative of 8sin^2(x)*cos(x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
     2          
8*sin (x)*cos(x)
$$8 \sin^{2}{\left(x \right)} \cos{\left(x \right)}$$
(8*sin(x)^2)*cos(x)
Detail solution
  1. Apply the product rule:

    ; to find :

    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:

    ; to find :

    1. The derivative of cosine is negative sine:

    The result is:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
       3            2          
- 8*sin (x) + 16*cos (x)*sin(x)
$$- 8 \sin^{3}{\left(x \right)} + 16 \sin{\left(x \right)} \cos^{2}{\left(x \right)}$$
The second derivative [src]
   /       2           2   \       
-8*\- 2*cos (x) + 7*sin (x)/*cos(x)
$$- 8 \left(7 \sin^{2}{\left(x \right)} - 2 \cos^{2}{\left(x \right)}\right) \cos{\left(x \right)}$$
The third derivative [src]
  /        2           2   \       
8*\- 20*cos (x) + 7*sin (x)/*sin(x)
$$8 \left(7 \sin^{2}{\left(x \right)} - 20 \cos^{2}{\left(x \right)}\right) \sin{\left(x \right)}$$