Class 12 Continuity And Differentiability · Short Answer2 Markslogarithmic_differentiation
Class 12 Maths · Continuity And Differentiability · Short Answer #52
For y=x^(1/x), x>0, find y′ at x=1.
✅ Step-by-Step Solution
Final Answer: 1
- Take logarithms: ln y=(ln x)/x.
- Differentiate to get y′/y=(1−ln x)/x², hence y′=x^(1/x)(1−ln x)/x².
- At x=1, y′=1·(1−0)=1.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Take logarithms: ln y=(ln x)/x.
- [1 mark] Differentiate to get y′/y=(1−ln x)/x², hence y′=x^(1/x)(1−ln x)/x².
- [0.5 marks] At x=1, y′=1·(1−0)=1.
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