NCERT Class 12 · Ch 5 Exercise 5.3 · Q11
NCERT Class 12 Maths · Chapter 5 Continuity And Differentiability · Exercise 5.3 Question 11
Differentiate y=cos⁻¹((1−x²)/(1+x²)), 0<x<1.
💡 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: \(\frac{2}{x^{2} + 1}\)
- On 0<x<1, the principal inverse branch gives y=2tan⁻¹x.
- Differentiate the equivalent expression using the chain rule to get y′=\(\frac{2}{x^{2} + 1}\). The stated interval ensures the branch and denominator are valid.
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