Mister Exam

Derivative of 4sin(4x)+1

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
4*sin(4*x) + 1
$$4 \sin{\left(4 x \right)} + 1$$
4*sin(4*x) + 1
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. 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:

    2. The derivative of the constant is zero.

    The result is:


The answer is:

The graph
The first derivative [src]
16*cos(4*x)
$$16 \cos{\left(4 x \right)}$$
The second derivative [src]
-64*sin(4*x)
$$- 64 \sin{\left(4 x \right)}$$
The third derivative [src]
-256*cos(4*x)
$$- 256 \cos{\left(4 x \right)}$$