Find the derivative of $LaTeX: \displaystyle f(x) = \sin^{-1}{\left(2 x \right)}$ .

Using the chain rule gives $LaTeX: \displaystyle f'(x) = \frac{df}{du}\frac{du}{dx}$ where $LaTeX: \displaystyle f(u) = \sin^{-1}{\left(u \right)}$ and $LaTeX: \displaystyle u = 2 x$ gives $LaTeX: \displaystyle f'(x) = \frac{2}{\sqrt{1 - 4 x^{2}}}$