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CUET · MATHS · PYQ PAPER 2023

If \((x+1) e^y=1\), then :

  1. A \(\frac{d^2 y}{d x^2}=y^2\)
  2. B \(\frac{d^2 y}{d x^2}=\left(\frac{d y}{d x}\right)^2\)
  3. C \(\frac{d^2 y}{d x^2}=-y^2\)
  4. D \(\frac{d^2 y}{d x^2}=\frac{d y}{d x}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{d^2 y}{d x^2}=\left(\frac{d y}{d x}\right)^2\)

Step-by-step Solution

Detailed explanation

Given \((x+1) e^y=1\). Differentiating implicitly w.r.t. \(x\): \(1 \cdot e^y + (x+1)e^y \frac{dy}{dx} = 0\). Substitute \((x+1)e^y=1\): \(e^y + 1 \cdot \frac{dy}{dx} = 0 \implies \frac{dy}{dx} = -e^y\). Differentiating \(\frac{dy}{dx} = -e^y\) w.r.t. \(x\):…