Mister Exam

Derivative of 3x-sin3x

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
3*x - sin(3*x)
$$3 x - \sin{\left(3 x \right)}$$
3*x - sin(3*x)
Detail solution
  1. Differentiate term by term:

    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:

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

      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:

      So, the result is:

    The result is:


The answer is:

The graph
The first derivative [src]
3 - 3*cos(3*x)
$$3 - 3 \cos{\left(3 x \right)}$$
The second derivative [src]
9*sin(3*x)
$$9 \sin{\left(3 x \right)}$$
The third derivative [src]
27*cos(3*x)
$$27 \cos{\left(3 x \right)}$$