Find `(dy)/(dx)` in each of the following: `e^(x-y)=log(x/y)`

Explanation

Given as `e^{x-y}=\log (x / y)`



Differentiating the equation on both sides with respect to `x`,
$$
\begin{aligned}
&\frac{d}{d x}\left(e^{x-y}\right)=\frac{d}{d x}\left\{\log \left(\frac{x}{y}\right)\right\} \\
&\Rightarrow e^{(x-y)} \frac{d}{d x}(x-y)=\frac{1}{\left(\frac{x}{y}\right)} \times \frac{d}{d x}\left(\frac{x}{y}\right)
\end{aligned}
...