# What is the derivative of cos (2x)?

$- 2 \sin \left(2 x\right)$
if $y = f \left(g \left(x\right)\right)$
then $y ' = f ' \left(g \left(x\right)\right) \cdot g ' \left(x\right)$ by the chain rule, or the derivative of the outside function times the derivative of the inside function.
So the derivative of $\cos \left(2 x\right)$ is $- \sin \left(2 x\right)$ times the derivative of the inside, so it is $- 2 \sin \left(2 x\right)$.