Mister Exam

Derivative of sin5x+cos(2x-3)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
sin(5*x) + cos(2*x - 3)
$$\sin{\left(5 x \right)} + \cos{\left(2 x - 3 \right)}$$
sin(5*x) + cos(2*x - 3)
Detail solution
  1. Differentiate term by term:

    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:

    4. Let .

    5. The derivative of cosine is negative sine:

    6. 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:

    The result is:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
-2*sin(2*x - 3) + 5*cos(5*x)
$$- 2 \sin{\left(2 x - 3 \right)} + 5 \cos{\left(5 x \right)}$$
The second derivative [src]
-(4*cos(-3 + 2*x) + 25*sin(5*x))
$$- (25 \sin{\left(5 x \right)} + 4 \cos{\left(2 x - 3 \right)})$$
The third derivative [src]
-125*cos(5*x) + 8*sin(-3 + 2*x)
$$8 \sin{\left(2 x - 3 \right)} - 125 \cos{\left(5 x \right)}$$
The graph
Derivative of sin5x+cos(2x-3)