First slide

Derivatives

Question

$\frac{d}{d x} \{\log (x + \sqrt{x^{2} + 1})\} =$

Moderate

A

$\frac{1}{1 + x^{2}}$
B

$\frac{1}{\sqrt{1 + x^{2}}}$
C

$- \frac{1}{\sqrt{1 + x^{2}}}$
D

$\sqrt{1 + x^{2}}$

Solution

$\frac{d}{d x} [\log (x + \sqrt{x^{2} + 1})] = \frac{d}{d x} (\sinh^{- 1} x) = \frac{1}{\sqrt{x^{2} + 1}}$

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