Mister Exam

Derivative of -2sin(4x+2)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
-2*sin(4*x + 2)
$$- 2 \sin{\left(4 x + 2 \right)}$$
-2*sin(4*x + 2)
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]
-8*cos(4*x + 2)
$$- 8 \cos{\left(4 x + 2 \right)}$$
The second derivative [src]
32*sin(2*(1 + 2*x))
$$32 \sin{\left(2 \left(2 x + 1\right) \right)}$$
The third derivative [src]
128*cos(2*(1 + 2*x))
$$128 \cos{\left(2 \left(2 x + 1\right) \right)}$$
The graph
Derivative of -2sin(4x+2)