Answer
$\frac{\ln\sqrt[3]{x}}{3\sqrt[3] {x^{2}}}-\frac{\ln\sqrt{x}}{2\sqrt x}$
Work Step by Step
$\frac{dy}{dx}$ = $\ln\sqrt[3]{x}\frac{d}{dx}(\sqrt[3] x) - \ln\sqrt{x}\frac{d}{dx}(\sqrt x)$
$\frac{dy}{dx}$ = $\ln\sqrt[3]{x}(\frac{1}{3\sqrt[3] {x^{2}}}) - \ln\sqrt{x}(\frac{1}{2\sqrt x})$
$\frac{dy}{dx}$ = $\frac{\ln\sqrt[3]{x}}{3\sqrt[3] {x^{2}}}-\frac{\ln\sqrt{x}}{2\sqrt x}$
