Answer
$2x\ln|x|-\frac{x}{\sqrt 2}\ln|x|$
Work Step by Step
$\frac{dy}{dx}$ = $\ln\sqrt {x^{2}}\frac{d}{dy}(x^{2})-\ln\sqrt {\frac{x^{2}}{2}}\frac{d}{dy}(\frac{x^{2}}{2})$
$\frac{dy}{dx}$ = $\ln|x|(2x)-\frac{1}{\sqrt 2}\ln|x|(x)$
$\frac{dy}{dx}$ = $2x\ln|x|-\frac{x}{\sqrt 2}\ln|x|$
