Compute the derivative of the given function

by RoRi

September 21, 2015

Compute the derivative of the function

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

Using the chain rule,

$\begin{align*} f'(x) &= \sqrt{1+x^2} + x (2x)\left(\frac{1}{2}\right)(1+x^2)^{-\frac{1}{2}} \\[8pt] &= \frac{1+2x^2}{\sqrt{1+x^2}}. \end{align*}$

Stumbling Robot