Question

Differentiate the equation
$e^{x-y}=\log \left(\frac{x}{y}\right)$

Answer 1

$\begin{array}{c}{e}^{x-y}=\log x-\log y\\ e^x{e}^y=\log x-\log y\end{array}$
Differentiate,
$\begin{array}{c}{e}^{-y}{e}^x-e^{-y}{e}^x\frac{dy}{dx}=\frac{1}{x}-\frac{1}{y}\frac{dy}{dx}\\ e^{x-y}-\frac{1}{x}=\frac{dy}{dx}\left(e^{x-y}-\frac{1}{y}\right)\\ \frac{dy}{dx}=\frac{e^{x-y}-\frac{1}{x}}{e^{x-y}-\frac{1}{y}}\end{array}$