NCERT Class 12 · Ch 5 Exercise 5.7 · Q16
NCERT Class 12 Maths · Chapter 5 Continuity And Differentiability · Exercise 5.7 Question 16
If eʸ(x+1)=1, prove y″=(y′)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: y′=−1/(x+1); y″=1/(x+1)²=(y′)².
- The real equation requires x>−1. Take logs: y=−log(x+1).
- Differentiate once and twice to obtain the stated formulas, and square the first derivative.
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