CUET · MATHS · PYQ PAPER 2023
If \(x^2+2 x y+y^3=10\), then the value of \(\frac{d y}{d x}\) is:
- A \(\frac{x^2+y^2}{x^2-y^2}\)
- B \(-\frac{2(x+y)}{2 x+3 y^2}\)
- C \(\frac{2(x-y)}{2 x-3 y^2}\)
- D \(\frac{2(x+y)}{x-y}\)
Answer & Solution
Correct Answer
(B) \(-\frac{2(x+y)}{2 x+3 y^2}\)
Step-by-step Solution
Detailed explanation
\(\frac{d}{d x}(x^2+2 x y+y^3) = \frac{d}{d x}(10)\) \(2x + 2(1 \cdot y + x \cdot \frac{d y}{d x}) + 3y^2 \frac{d y}{d x} = 0\) \(2x + 2y + 2x \frac{d y}{d x} + 3y^2 \frac{d y}{d x} = 0\) \((2x + 3y^2) \frac{d y}{d x} = -2x - 2y\) \(\frac{d y}{d x} = -\frac{2x + 2y}{2x + 3y^2}\)…
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