NCERT Class 12 · Ch 5 Miscellaneous Exercise · Q13
NCERT Class 12 Maths · Chapter 5 Continuity And Differentiability · Miscellaneous Exercise Question 13
Differentiate y=sin⁻¹x+sin⁻¹√(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: 0.
- Set u=sin⁻¹x∈(0,π/2). Then √(1−x²)=cos u and sin⁻¹(cos u)=π/2−u.
- Thus y=π/2 is constant and dy/dx=0.
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