Mister Exam

Derivative of cos(9x-10)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
cos(9*x - 10)
$$\cos{\left(9 x - 10 \right)}$$
d                
--(cos(9*x - 10))
dx               
$$\frac{d}{d x} \cos{\left(9 x - 10 \right)}$$
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 graph
The first derivative [src]
-9*sin(9*x - 10)
$$- 9 \sin{\left(9 x - 10 \right)}$$
The second derivative [src]
-81*cos(-10 + 9*x)
$$- 81 \cos{\left(9 x - 10 \right)}$$
The third derivative [src]
729*sin(-10 + 9*x)
$$729 \sin{\left(9 x - 10 \right)}$$
The graph
Derivative of cos(9x-10)