Class 12 Continuity And Differentiability · Short Answer2 Marksimplicit_differentiation
Class 12 Maths · Continuity And Differentiability · Short Answer #50
If (x²+y²)²=xy, find dy/dx where the implicit-function denominator is nonzero.
✅ Step-by-Step Solution
Final Answer: [y−4x(x²+y²)]/[4y(x²+y²)−x]
- Implicit differentiation gives 4(x²+y²)(x+yy′)=y+xy′.
- Collect y′ terms: [4y(x²+y²)−x]y′=y−4x(x²+y²).
- Divide by the nonzero coefficient to obtain y′=[y−4x(x²+y²)]/[4y(x²+y²)−x].
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Implicit differentiation gives 4(x²+y²)(x+yy′)=y+xy′.
- [1 mark] Collect y′ terms: [4y(x²+y²)−x]y′=y−4x(x²+y²).
- [0.5 marks] Divide by the nonzero coefficient to obtain y′=[y−4x(x²+y²)]/[4y(x²+y²)−x].
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