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

Jan 25, 2015

$2 \cdot \cos \left(2 x\right)$

I would use the Chain Rule:

First derive $\sin$ and then the argument $2 x$ to get:
$\cos \left(2 x\right) \cdot 2$

Jun 20, 2018

$2 \cos 2 x$

#### Explanation:

The key realization is that we have a composite function, which can be differentiated with the help of the Chain Rule

$f ' \left(g \left(x\right)\right) \cdot g ' \left(x\right)$

We essentially have a composite function

$f \left(g \left(x\right)\right)$ where

$f \left(x\right) = \sin x \implies f ' \left(x\right) = \cos x$ and $g \left(x\right) = 2 x \implies g ' \left(x\right) = 2$

We know all of the values we need to plug in, so let's do that. We get

$\cos \left(2 x\right) \cdot 2$

$\implies 2 \cos 2 x$

Hope this helps!