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  4. Let f(x) = log (x + √x2 + 1) , then f'(x) equals

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Q. Let $f(x) = \log (x + \sqrt{x^2 + 1})$ , then $f'(x)$ equals

Limits and Derivatives

Solution:

$f'\left(x\right) = \frac{1}{x+\sqrt{x^{2}+1}} \left[ 1+ \frac{1.2 x}{2\sqrt{x^{2} + 1}} \right]$
$ = \frac{1}{\sqrt{x^{2}+1}}$