Mister Exam

Derivative of sin(5*x+4)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
sin(5*x + 4)
$$\sin{\left(5 x + 4 \right)}$$
sin(5*x + 4)
Detail solution
  1. Let .

  2. The derivative of sine is cosine:

  3. 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:

  4. Now simplify:


The answer is:

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