Class 12 Continuity And Differentiability · Short Answer2 Marksimplicit_differentiation
Class 12 Maths · Continuity And Differentiability · Short Answer #120
If sin²y+cos(xy)=K is constant, find dy/dx at x=1,y=π/4.
✅ Step-by-Step Solution
Final Answer: π/[4(√2−1)]
- Implicit differentiation gives 2sin y cos y·y′−sin(xy)(y+xy′)=0.
- At (1,π/4), this becomes y′−(√2/2)(π/4+y′)=0. Hence (1−√2/2)y′=π√2/8.
- Solving gives y′=π/[4(√2−1)].
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Implicit differentiation gives 2sin y cos y·y′−sin(xy)(y+xy′)=0.
- [1 mark] At (1,π/4), this becomes y′−(√2/2)(π/4+y′)=0. Hence (1−√2/2)y′=π√2/8.
- [0.5 marks] Solving gives y′=π/[4(√2−1)].
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