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2*sin(x)*cos(x)

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

Function f() - derivative -N order at the point
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The graph:

from to

Piecewise:

The solution

You have entered [src]
2*sin(x)*cos(x)
$$2 \sin{\left(x \right)} \cos{\left(x \right)}$$
d                  
--(2*sin(x)*cos(x))
dx                 
$$\frac{d}{d x} 2 \sin{\left(x \right)} \cos{\left(x \right)}$$
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. The derivative of cosine is negative sine:

      ; to find :

      1. The derivative of sine is cosine:

      The result is:

    So, the result is:

  2. Now simplify:


The answer is:

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