Question

(1 +x²) cos x

Answer 1

$$\begin{gathered} \mathrm{Let}u=1+x^2;v=\cos x \\ \mathrm{Then},u\text{'}=2x;v\text{'}=-\sin x \\ \text{Using the product rule:} \\ \frac{d}{dx}\left(uv\right)=uv\text{'}+vu\text{'} \\ \frac{d}{dx}\left[\left(1+x^2\right)\left(\cos x\right)\right]=\left(1+x^2\right)\left(-\sin x\right)+\left(\cos x\right)\left(2x\right) \\ =-\sin x-x^2\sin x+2x\cos x \end{gathered}$$