NCERT Class 12 · Ch 5 Miscellaneous Exercise · Q17
NCERT Class 12 Maths · Chapter 5 Continuity And Differentiability · Miscellaneous Exercise Question 17
For x=a(cos t+t sin t), y=a(sin t−t cos t), find d²y/dx².
💡 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: \(\frac{\sec^{3}{\left(t \right)}}{a t}\) where at cos t≠0.
- dx/dt=at cos t and dy/dt=at sin t, so dy/dx=tan t where dx/dt≠0.
- Differentiate the slope with respect to t and divide again by dx/dt: y″=sec²t/(at cos t)=1/(at cos³t).
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