#### Answer

$\frac{d}{dx}\sin^{-1}\left(\frac{1}{x}\right) = \frac{-1}{|x|\sqrt {x^2-1}}$

#### Work Step by Step

Chain Rule:
$\frac{d}{dx}\sin^{-1}\left(\frac{1}{x}\right) = \frac{1}{\sqrt {1-(\frac{1}{x})^2}} \times \frac{-1}{x^2} = \frac{-1}{x^2\sqrt {1-\left(\frac{1}{x}\right)^2}} = \frac{-1}{|x|\sqrt {x^2-1}}$