NCERT Class 12 · Ch 5 Exercise 5.3 · Q14
NCERT Class 12 Maths · Chapter 5 Continuity And Differentiability · Exercise 5.3 Question 14
Differentiate y=sin⁻¹(2x√(1−x²)), −1/√2<x<1/√2.
💡 Concept Hints
- Identify the domain and the inner and outer functions, or the relevant one-sided limits.
- Apply the appropriate differentiation or limit rule, keep all chain factors, and check exceptional points.
✅ Step-by-Step Solution
Final Answer: \(\frac{2}{\sqrt{1 - x^{2}}}\)
- On −1/√2<x<1/√2, the principal inverse branch gives y=2sin⁻¹x.
- Differentiate the equivalent expression using the chain rule to get y′=\(\frac{2}{\sqrt{1 - x^{2}}}\). The stated interval ensures the branch and denominator are valid.
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