Mister Exam

Derivative of y(x)=-sin(5x+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. 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. 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:

    So, the result is:

  2. 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)
$$125 \cos{\left(5 x + 4 \right)}$$
The graph
Derivative of y(x)=-sin(5x+4)