Browse Questions

# Differentiate the following w.r.t. $x: \large \frac {\cos x}{\log x}$,$\; x > 0$

$\begin{array}{1 1} - \large \frac{x\; \sin x \log x + \cos x}{x\;(\log x)^2} \\ \large \frac{x\; \sin x \log x + \cos x}{x\;(\log x)^2} \\ - \large \frac{x\; \sin x \log x - \cos x}{x\;\log x} \\ - \large \frac{x\; \sin x \log x + \cos x}{x\;\log x}\end{array}$

Toolbox:
• According to the Quotient Rule for differentiation, given two functions $u$ and $v,\; \large (\frac{u}{v})\;$$' = \large \frac{1}{v^2} (v\;u' - u\;v') • \; \large \frac{d(\log x)}{dx}$$=\large\frac{1}{x}$
• $\; \large \frac{d(cosx)}{dx} $$=-sinx Given y = \large \frac {\cos x}{\log x}. This is of the form \large \frac{u}{v} where u = \cos x and v = \log x If u = \cos x, u' = -\sin x If u = \log x, u' = \large \frac{1}{x} According to the Quotient Rule for differentiation, given two functions u and v,\; \large (\frac{u}{v})\;$$' = \large \frac{1}{v^2}$ $(v\;u' - u\;v')$