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

##### 1 Answer

Jan 27, 2016

#### 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

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

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