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Class 12 Continuity And Differentiability · Mcq Single Correct1 Marksimplicit_differentiation

Class 12 Maths · Continuity And Differentiability · Mcq Single Correct #15

If (x²+y²)²=xy, find dy/dx where a differentiable branch exists and 4y(x²+y²)−x≠0.

(A) [y+4x(x²+y²)]/[4y(x²+y²)−x]
(B) [y−4x(x²+y²)]/[x+4(x²+y²)]
(C) [y−4x(x²+y²)]/[4y(x²+y²)−x]
(D) [4y(x²+y²)−x]/[y−4x(x²+y²)]

✅ Step-by-Step Solution

Final Answer: Option (C): [y−4x(x²+y²)]/[4y(x²+y²)−x]

Differentiate: 4(x²+y²)(x+yy′)=y+xy′. Collecting gives [4y(x²+y²)−x]y′=y−4x(x²+y²), yielding option c.

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