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CUET · MATHS · PYQ PAPER 2025

If \(e^x+e^y=e^{x+y}\), then \(\frac{d y}{d x}=\)

  1. A \(e^{x-y}\)
  2. B \(e^{y-x}\)
  3. C \(-e^{y-x}\)
  4. D \(e^{x+y}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(-e^{y-x}\)

Step-by-step Solution

Detailed explanation

\(\frac{e^x}{e^{x+y}} + \frac{e^y}{e^{x+y}} = \frac{e^{x+y}}{e^{x+y}}\) \(e^{-y} + e^{-x} = 1\) \(\frac{d}{dx}(e^{-y}) + \frac{d}{dx}(e^{-x}) = \frac{d}{dx}(1)\) \(-e^{-y}\frac{dy}{dx} - e^{-x} = 0\) \(-e^{-y}\frac{dy}{dx} = e^{-x}\) \(\frac{dy}{dx} = \frac{e^{-x}}{-e^{-y}}\)…