Question

If \(y^x = e^{y - x}\), then \(\frac{dy}{dx}\) is equal to:

• A. \(\frac{1 + \log y}{y \log y}\)
• B. \(\frac{(1 + \log y)^2}{y \log y}\)
• C. \(\frac{1 + \log y}{(\log y)^2}\)
• D. \(\frac{(1 + \log y)^2}{\log y}\)

Hint:

For equations where variables appear both in the base and exponent, apply logarithm first to simplify the expression before differentiating.

Answer 1

The Correct Option is D