Mister Exam

Other calculators

Derivative of -cos(3*x)-sin(3*x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
-cos(3*x) - sin(3*x)
$$- \sin{\left(3 x \right)} - \cos{\left(3 x \right)}$$
-cos(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. 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]
-3*cos(3*x) + 3*sin(3*x)
$$3 \sin{\left(3 x \right)} - 3 \cos{\left(3 x \right)}$$
The second derivative [src]
9*(cos(3*x) + sin(3*x))
$$9 \left(\sin{\left(3 x \right)} + \cos{\left(3 x \right)}\right)$$
The third derivative [src]
27*(-sin(3*x) + cos(3*x))
$$27 \left(- \sin{\left(3 x \right)} + \cos{\left(3 x \right)}\right)$$