Compute the derivative of log ((1+x²)^1/2)

by RoRi

November 1, 2015

Compute the derivative of

$f(x) = \log \sqrt{1+x^2}.$

Using the chain rule we have,

$\begin{align*} f'(x) &= \left(\frac{1}{\sqrt{1+x^2}}\right)\left(\frac{1}{2\sqrt{1+x^2}}\right)(2x)\\ &= \frac{x}{1+x^2}. \end{align*}$

Stumbling Robot