Class 12 Continuity And Differentiability · Short Answer2 Marksimplicit_differentiation
Class 12 Maths · Continuity And Differentiability · Short Answer #49
For y=(x+√(x²−1))² with |x|>1, show (x²−1)(y′)²=4y².
✅ Step-by-Step Solution
Final Answer: Identity proved for |x|>1.
- Differentiate: y′=2(x+√(x²−1))[1+x/√(x²−1)].
- The bracket is (x+√(x²−1))/√(x²−1), so y′=2y/√(x²−1).
- Squaring and multiplying by x²−1 gives the required identity.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Differentiate: y′=2(x+√(x²−1))[1+x/√(x²−1)].
- [1 mark] The bracket is (x+√(x²−1))/√(x²−1), so y′=2y/√(x²−1).
- [0.5 marks] Squaring and multiplying by x²−1 gives the required identity.
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