Mister Exam

Derivative of sin(6*x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
sin(6*x)
$$\sin{\left(6 x \right)}$$
d           
--(sin(6*x))
dx          
$$\frac{d}{d x} \sin{\left(6 x \right)}$$
Detail solution
  1. Let .

  2. The derivative of sine is cosine:

  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:


The answer is:

The graph
The first derivative [src]
6*cos(6*x)
$$6 \cos{\left(6 x \right)}$$
The second derivative [src]
-36*sin(6*x)
$$- 36 \sin{\left(6 x \right)}$$
The third derivative [src]
-216*cos(6*x)
$$- 216 \cos{\left(6 x \right)}$$
The graph
Derivative of sin(6*x)