Mister Exam

Derivative of 2sin²xcosx

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
     2          
2*sin (x)*cos(x)
$$2 \sin^{2}{\left(x \right)} \cos{\left(x \right)}$$
d /     2          \
--\2*sin (x)*cos(x)/
dx                  
$$\frac{d}{d x} 2 \sin^{2}{\left(x \right)} \cos{\left(x \right)}$$
Detail solution
  1. The derivative of a constant times a function is the constant times the derivative of the function.

    1. Apply the product rule:

      ; to find :

      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:

      ; to find :

      1. The derivative of cosine is negative sine:

      The result is:

    So, the result is:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
       3           2          
- 2*sin (x) + 4*cos (x)*sin(x)
$$- 2 \sin^{3}{\left(x \right)} + 4 \sin{\left(x \right)} \cos^{2}{\left(x \right)}$$
The second derivative [src]
   /       2           2   \       
-2*\- 2*cos (x) + 7*sin (x)/*cos(x)
$$- 2 \cdot \left(7 \sin^{2}{\left(x \right)} - 2 \cos^{2}{\left(x \right)}\right) \cos{\left(x \right)}$$
The third derivative [src]
  /        2           2   \       
2*\- 20*cos (x) + 7*sin (x)/*sin(x)
$$2 \cdot \left(7 \sin^{2}{\left(x \right)} - 20 \cos^{2}{\left(x \right)}\right) \sin{\left(x \right)}$$
The graph
Derivative of 2sin²xcosx