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

Explanation

To find \(\frac{dy}{dx}\) for the equation \(e^{(x-y)} = \log\left(\frac{x}{y}\right)\), we will differentiate both sides with respect to \(x\). Here’s a step-by-step solution:

### Step 1: Differentiate both sides
We start with the equation:
\[ e^{(x-y)} = \log\left(\frac{x}{y}\right) \]
Differentiating the left side using the chain rule:
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