What is $\frac{d}{dx}\left(\sin^{-1}{\left(2 x \right)}\right)$ for $\lvert x \rvert < \frac{1}{2}$?

Explanation

1. 01

   $\frac{d}{dx}\sin^{-1} u = \frac{u'}{\sqrt{1 - u^{2}}}$ with $u = 2x$.

2. 02

   $\frac{2}{\sqrt{1 - 4x^{2}}}$.