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CUET · MATHS · PYQ PAPER 2025

If \(y=x \sin y\), then \(\frac{d y}{d x}\) is:

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

Answer & Solution

Correct Answer

(B) \(\frac{\sin ^2 y}{\sin y-y \cos y}\)

Step-by-step Solution

Detailed explanation

\(\frac{d}{dx}(y) = \frac{d}{dx}(x \sin y)\) \(\frac{dy}{dx} = \sin y + x \cos y \frac{dy}{dx}\) \(\frac{dy}{dx}(1 - x \cos y) = \sin y\) \(\frac{dy}{dx} = \frac{\sin y}{1 - x \cos y}\) From \(y = x \sin y\), we have \(x = \frac{y}{\sin y}\).…