$\begin{align}  & y=x\sin x \\ & \frac{dy}{dx}=x\frac{d}{dx}(\sin x)+\sin x\frac{d}{dx}(x) \\ & \frac{dy}{dx}=x\cos x+\sin x \\ & \text{when }x=\tfrac{\pi }{2} \\ & \frac{dy}{dx}\left| _{x=\tfrac{\pi }{2}}=\frac{\pi }{2}\cos \frac{\pi }{2}+\sin \frac{\pi }{2} \right. \\\end{align}$