Mister Exam

Derivative of -4sin(4x+180)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
-4*sin(4*x + 180)
$$- 4 \sin{\left(4 x + 180 \right)}$$
-4*sin(4*x + 180)
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 sine is cosine:

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

      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 the constant is zero.

        The result is:

      The result of the chain rule is:

    So, the result is:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
-16*cos(4*x + 180)
$$- 16 \cos{\left(4 x + 180 \right)}$$
The second derivative [src]
64*sin(4*(45 + x))
$$64 \sin{\left(4 \left(x + 45\right) \right)}$$
The third derivative [src]
256*cos(4*(45 + x))
$$256 \cos{\left(4 \left(x + 45\right) \right)}$$
The graph
Derivative of -4sin(4x+180)