Mister Exam

Derivative of 3sin(2x)−5cos(2x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
3*sin(2*x) - 5*cos(2*x)
$$3 \sin{\left(2 x \right)} - 5 \cos{\left(2 x \right)}$$
3*sin(2*x) - 5*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. 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:

    The result is:


The answer is:

The graph
The first derivative [src]
6*cos(2*x) + 10*sin(2*x)
$$10 \sin{\left(2 x \right)} + 6 \cos{\left(2 x \right)}$$
The second derivative [src]
4*(-3*sin(2*x) + 5*cos(2*x))
$$4 \left(- 3 \sin{\left(2 x \right)} + 5 \cos{\left(2 x \right)}\right)$$
3-я производная [src]
-8*(3*cos(2*x) + 5*sin(2*x))
$$- 8 \left(5 \sin{\left(2 x \right)} + 3 \cos{\left(2 x \right)}\right)$$
The third derivative [src]
-8*(3*cos(2*x) + 5*sin(2*x))
$$- 8 \left(5 \sin{\left(2 x \right)} + 3 \cos{\left(2 x \right)}\right)$$