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CBSE Class 12 Mathematics 2026 Supplementary Paper 65/7/2 · Q273 Markslogarithmic_differentiation

CBSE Class 12 Mathematics 2026 Supplementary Paper 65/7/2 · Question 27 (Continuity And Differentiability)

For \(y=(x+\sqrt{x^2-a^2})^n\), show \(y\prime=ny/\sqrt{x^2-a^2}\) on regular real branches where the power is defined and the base is nonzero.

✅ Step-by-Step Solution

Final Answer: y′=ny/√(x²−a²).
  1. Write u=x+√(x²−a²). On a regular branch u′=1+x/√(x²−a²)=u/√(x²−a²).
  2. Use the power rule on y=uⁿ.
  3. Then y′=nu^(n−1)u′=ny/√(x²−a²).

📋 CBSE Stepwise Marking Scheme

  • [0.5 marks] Write u=x+√(x²−a²). On a regular branch u′=1+x/√(x²−a²)=u/√(x²−a²).
  • [2 marks] Use the power rule on y=uⁿ.
  • [0.5 marks] Then y′=nu^(n−1)u′=ny/√(x²−a²).

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