If $f(x) = \sin^{-1}{\left(x \right)}$, what is $f'\left(\frac{1}{2}\right)$?

Explanation

1. 01

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

2. 02

   At $\frac{1}{2}$: $\frac{1}{\sqrt{3/4}} = \frac{2}{\sqrt{3}}$.