Question

Find the derivatives of $x\cos x$

Answer 1

$y=x\cos x$

By using product rule of differentiation,

$\frac{d(u.v)}{dx}=v\frac{du}{dx}+u\frac{dv}{dx}$

$\frac{dy}{dx}=x\frac{d}{dx}\left(\cos x\right)+\cos x\frac{d}{dx}\left(x\right)$

$\frac{dy}{dx}=-x\sin x+\cos x$