What is $\frac{d}{dx}\left(\log{\left(x + \sqrt{x^{2} + 1} \right)}\right)$?

Explanation

1. 01

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

2. 02

   $\frac{u'}{u} = \frac{1}{\sqrt{x^{2} + 1}}$.