Mister Exam

Derivative of 2cos(2x)-2sin(2x)

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

The graph:

from to

Piecewise:

The solution

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2*cos(2*x) - 2*sin(2*x)
$$- 2 \sin{\left(2 x \right)} + 2 \cos{\left(2 x \right)}$$
2*cos(2*x) - 2*sin(2*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. Let .

      2. The derivative of cosine is negative sine:

      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 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:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
-4*cos(2*x) - 4*sin(2*x)
$$- 4 \sin{\left(2 x \right)} - 4 \cos{\left(2 x \right)}$$
The second derivative [src]
8*(-cos(2*x) + sin(2*x))
$$8 \left(\sin{\left(2 x \right)} - \cos{\left(2 x \right)}\right)$$
The third derivative [src]
16*(cos(2*x) + sin(2*x))
$$16 \left(\sin{\left(2 x \right)} + \cos{\left(2 x \right)}\right)$$