Question:
Differentiate the following w.r.t. x:
$\frac{\cos x}{\log x}, x>0$
Solution:
Let $y=\frac{\cos x}{\log x}$
By using the quotient rule, we obtainc
$\frac{d y}{d x}=\frac{\frac{d}{d x}(\cos x) \times \log x-\cos x \times \frac{d}{d x}(\log x)}{(\log x)^{2}}$
$=\frac{-\sin x \log x-\cos x \times \frac{1}{x}}{(\log x)^{2}}$
$=\frac{-[x \log x \cdot \sin x+\cos x]}{x(\log x)^{2}}, x>0$
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