Mister Exam

Derivative of -4sinxcosx

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
-4*sin(x)*cos(x)
$$- 4 \sin{\left(x \right)} \cos{\left(x \right)}$$
(-4*sin(x))*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. The derivative of sine is cosine:

      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]
       2           2   
- 4*cos (x) + 4*sin (x)
$$4 \sin^{2}{\left(x \right)} - 4 \cos^{2}{\left(x \right)}$$
The second derivative [src]
16*cos(x)*sin(x)
$$16 \sin{\left(x \right)} \cos{\left(x \right)}$$
The third derivative [src]
   /   2         2   \
16*\cos (x) - sin (x)/
$$16 \left(- \sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}\right)$$