$\begin{align}  & y=x{{\sin }^{-1}}x \\ & \text{Using product rule} \\ & \frac{dy}{dx}=x\frac{d}{dx}({{\sin }^{-1}}x)+{{\sin }^{-1}}x\frac{d}{dx}(x) \\ & \frac{dy}{dx}=x\frac{1}{\sqrt{1-{{x}^{2}}}}+{{\sin }^{-1}}x \\ & \frac{dy}{dx}=\frac{x}{\sqrt{1-{{x}^{2}}}}+{{\sin }^{-1}}x \\\end{align}$