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

1 Answer
Jan 27, 2016

#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)#