Mister Exam

Derivative of sin(x)*cos(x)

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

The graph:

from to


The solution

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

    ; to find :

    1. The derivative of sine is cosine:

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