CBSE Class 12 Mathematics 2026 Main Paper 65/3/2 · Q242 Marksparametric_derivatives
CBSE Class 12 Mathematics 2026 Main Paper 65/3/2 · Question 24 (Continuity And Differentiability)
If \(x=e^{t+1/t}\) and \(y=e^{t-1/t}\), find dy/dx at t=−2.
✅ Step-by-Step Solution
Final Answer: 5e/3.
- Differentiate to obtain dx/dt=(1−1/t²)e^(t+1/t) and dy/dt=(1+1/t²)e^(t−1/t).
- Divide to get [(t²+1)/(t²−1)]e^(−2/t).
- Substitute t=−2 to get 5e/3.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Differentiate to obtain dx/dt=(1−1/t²)e^(t+1/t) and dy/dt=(1+1/t²)e^(t−1/t).
- [1 mark] Divide to get [(t²+1)/(t²−1)]e^(−2/t).
- [0.5 marks] Substitute t=−2 to get 5e/3.
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