Mister Exam

Derivative of 5cos4x

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
5*cos(4*x)
$$5 \cos{\left(4 x \right)}$$
d             
--(5*cos(4*x))
dx            
$$\frac{d}{d x} 5 \cos{\left(4 x \right)}$$
Detail solution
  1. The derivative of a constant times a function is the constant times the derivative of the function.

    1. Let .

    2. The derivative of cosine is negative sine:

    3. Then, apply the chain rule. Multiply by :

      1. The derivative of a constant times a function is the constant times the derivative of the function.

        1. Apply the power rule: goes to

        So, the result is:

      The result of the chain rule is:

    So, the result is:


The answer is:

The graph
The first derivative [src]
-20*sin(4*x)
$$- 20 \sin{\left(4 x \right)}$$
The second derivative [src]
-80*cos(4*x)
$$- 80 \cos{\left(4 x \right)}$$
The third derivative [src]
320*sin(4*x)
$$320 \sin{\left(4 x \right)}$$
The graph
Derivative of 5cos4x