$\begin{align}  & y={{\log }_{a}}{{x}^{2}} \\ & \frac{dy}{dx}=\frac{\tfrac{d}{dx}({{x}^{2}})}{{{x}^{2}}}{{\log }_{e}}a=\frac{2x}{{{x}^{2}}}{{\log }_{e}}a \\ & \frac{dy}{dx}=\frac{2}{x}{{\log }_{e}}a \\\end{align}$