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

Apr 13, 2017

$f ' ' \left(x\right) = - 4 \sin 2 x$

#### Explanation:

Let $f \left(x\right) = \sin 2 x$.

By $\left(\sin x\right) ' = \cos x$ and Chain Rule,

$f ' \left(x\right) = \cos 2 x \cdot \left(2 x\right) ' = 2 \cos 2 x$

By $\left(\cos x\right) ' = - \sin x$ and Chain Rule,

$f ' ' \left(x\right) = - 2 \sin 2 x \cdot \left(2 x\right) ' = - 4 \sin 2 x$

I hope that this was clear.