Find the derivative of (x2 + 1) cos x.

1.	Find the derivative of (x2 + 1) cos x.
Answer» Let, y = (x² + 1) cos x ∴ \(\frac{dy}{dx}=\frac{d}{dx}[(x^2+1)cos\,x]\) \(=cos\,x\frac{d}{dx}(x^2+1)+(x^2+1)\frac{d}{dx}cos\,x\) \(=cos\,x.2x+(x^2+1).(-sin\,x)\) = 2x cos x − x² sin x − sin x

Answer»

Let,

y = (x² + 1) cos x

∴ \(\frac{dy}{dx}=\frac{d}{dx}[(x^2+1)cos\,x]\)

\(=cos\,x\frac{d}{dx}(x^2+1)+(x^2+1)\frac{d}{dx}cos\,x\)

\(=cos\,x.2x+(x^2+1).(-sin\,x)\)

= 2x cos x − x² sin x − sin x

Discussion