NCERT Class 12 · Ch 5 Exercise 5.3 · Q10
NCERT Class 12 Maths · Chapter 5 Continuity And Differentiability · Exercise 5.3 Question 10
Differentiate y=tan⁻¹((3x−x³)/(1−3x²)), −1/√3<x<1/√3.
💡 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: \(\frac{3}{x^{2} + 1}\)
- On −1/√3<x<1/√3, the principal inverse branch gives y=3tan⁻¹x.
- Differentiate the equivalent expression using the chain rule to get y′=\(\frac{3}{x^{2} + 1}\). The stated interval ensures the branch and denominator are valid.
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