What is the derivative of Csin(wx), where C and w are constants

I understand that the derivative of sin(wx) is (w)cos(wx), but what if there is a constant C in front? Thanks!!

First, use product rule: f'(x)g'(x) = f'(x)g(x) + f(x)g'(x)
At the same time, you are using the chain rule for sin(wx) as it is a composition of functions.

Suppose C is f(x), and sin(wx) is g(x)

Then:

0sin(wx) + Ccos(wx)w
= Cwcos(wx)

the derivative of a constant times a function is equal to the constant times the derivative of a function.

Symbolically:

(c f(x) ) ' = c * f ' (x)

so the derivative of C sin (wx) = Cw sin (wx).

Cw cos(wx)