Mister Exam

Derivative of cos(ax+b)

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

The graph:

from to


The solution

You have entered [src]
cos(a*x + b)
$$\cos{\left(a x + b \right)}$$
--(cos(a*x + b))
$$\frac{\partial}{\partial x} \cos{\left(a x + b \right)}$$
Detail solution
  1. Let .

  2. The derivative of cosine is negative sine:

  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 first derivative [src]
-a*sin(a*x + b)
$$- a \sin{\left(a x + b \right)}$$
The second derivative [src]
-a *cos(b + a*x)
$$- a^{2} \cos{\left(a x + b \right)}$$
The third derivative [src]
a *sin(b + a*x)
$$a^{3} \sin{\left(a x + b \right)}$$