If `y^x=e^(y-x)` , prove that `(dy)/(dx)=((1+logy)^2)/(logy)`

Explanation

To prove that \(\frac{dy}{dx} = \frac{(1 + \log y)^2}{\log y}\) given that \(y^x = e^{(y - x)}\), we will follow these steps:

### Step 1: Take the logarithm of both sides
Starting with the equation:
\[ y^x = e^{(y - x)} \]
Taking the natural logarithm of both sides gives:
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