$\begin{align}  & y=x{{\log }_{e}}x-x \\ & \frac{dy}{dx}=x\frac{d}{dx}({{\log }_{e}}x)-{{\log }_{e}}x\left( \frac{d}{dx}(x) \right)-\frac{d}{dx}(x) \\ & \frac{dy}{dx}=x\left( \frac{1}{x} \right)-{{\log }_{e}}x-1=1-{{\log }_{e}}x-1 \\ & \frac{dy}{dx}=-{{\log }_{e}}x \\\end{align}$