Question

How do you find the derivative of `cos (2x)`?

Answer 1

`f'(x) = - 2 sin(2x)`

Explanation:

You need to apply the chain rule:

`f(x) = cos(color(blue)(2x)) = cos(color(blue)(u)) " where " u = 2x`

Thus, you need to differentiate `cos u` and you need to differentiate `2x` and multiply those derivatives to obtain the derivative of `f(x)`:

`f'(x) = [cos u]' * [u]' = [cos u]' * [2x]'`

`= - sin color(blue)(u) * 2 = - sin (color(blue)(2x)) * 2 = - 2 sin(2x)`