Mister Exam

Derivative of y=sin(3x-9)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
sin(3*x - 9)
$$\sin{\left(3 x - 9 \right)}$$
d               
--(sin(3*x - 9))
dx              
$$\frac{d}{d x} \sin{\left(3 x - 9 \right)}$$
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]
3*cos(3*x - 9)
$$3 \cos{\left(3 x - 9 \right)}$$
The second derivative [src]
-9*sin(3*(-3 + x))
$$- 9 \sin{\left(3 \left(x - 3\right) \right)}$$
The third derivative [src]
-27*cos(3*(-3 + x))
$$- 27 \cos{\left(3 \left(x - 3\right) \right)}$$
The graph
Derivative of y=sin(3x-9)