Mister Exam

Derivative of 4sin3x+cos2x

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
4*sin(3*x) + cos(2*x)
$$4 \sin{\left(3 x \right)} + \cos{\left(2 x \right)}$$
4*sin(3*x) + cos(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 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. Let .

    3. The derivative of cosine is negative sine:

    4. 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:

    The result is:


The answer is:

The graph
The first derivative [src]
-2*sin(2*x) + 12*cos(3*x)
$$- 2 \sin{\left(2 x \right)} + 12 \cos{\left(3 x \right)}$$
The second derivative [src]
-4*(9*sin(3*x) + cos(2*x))
$$- 4 \left(9 \sin{\left(3 x \right)} + \cos{\left(2 x \right)}\right)$$
The third derivative [src]
4*(-27*cos(3*x) + 2*sin(2*x))
$$4 \left(2 \sin{\left(2 x \right)} - 27 \cos{\left(3 x \right)}\right)$$