Class 12 Continuity And Differentiability · Short Answer2 Markschain_and_product_rules
Class 12 Maths · Continuity And Differentiability · Short Answer #55
If f(x)=√(tan√x), find f′(π²/16).
✅ Step-by-Step Solution
Final Answer: 2/π
- Use the chain rule on f(x)=[tan(√x)]^(1/2).
- Then f′(x)=sec²√x/[4√x√(tan√x)]. At x=π²/16, √x=π/4, tan√x=1 and sec²√x=2.
- Thus f′(π²/16)=2/[4(π/4)]=2/π.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Use the chain rule on f(x)=[tan(√x)]^(1/2).
- [1 mark] Then f′(x)=sec²√x/[4√x√(tan√x)]. At x=π²/16, √x=π/4, tan√x=1 and sec²√x=2.
- [0.5 marks] Thus f′(π²/16)=2/[4(π/4)]=2/π.
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