Question

Differentiate the given function w.r.t. $x$.
$\frac{\cos x}{\log x},x>0$

Answer 1

Let $y=\frac{\cos x}{\log x},x>0$
Thus using quotient rule,
$\frac{dy}{dx}=\frac{\frac{d}{dx}\left(\cos x\right)\times \log x-\cos x\times \frac{d}{dx}\left(\log x\right)}{(\log x{)}^2}$
$=\frac{-\sin x\log x-\cos x\times \frac{1}{x}}{(\log x{)}^2}$
$=\frac{-[x\log x.\sin x+\cos x]}{x(\log x{)}^2},x>0$