$\begin{align}  & \frac{dy}{dx}=u\frac{dv}{dx}+v\frac{du}{dx} \\ & \frac{dy}{dx}=x\frac{d}{dx}(\sin x)+\sin x\frac{d}{dx}(x) \\ & \frac{dy}{dx}=x\cos x+\sin x \\ & \frac{dy}{dx}=\sin x+x\cos x \\\end{align}$