What is $\frac{d}{dx}\left(\tan^{-1}{\left(\frac{1}{x} \right)}\right)$ for $x > 0$?

Explanation

1. 01

   $\frac{u'}{1 + u^{2}}$ with $u = \frac{1}{x}$, $u' = -\frac{1}{x^{2}}$.

2. 02

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