Question

Differentiate the following function w.r.t x :
$\sqrt{x+\frac{1}{x}}$

Answer 1

$\frac{d}{dx}\left(\sqrt{x+\frac{1}{x}}\right)$

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

$=\frac{\left(\frac{x^2-1}{x^2}\right)}{\frac{2\sqrt{x^2+1}}{\sqrt{x}}}=\frac{(x^2-1)\sqrt{x}}{2x^2\sqrt{x^2+1}}$