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

Explanation

1. 01

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

2. 02

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