NCERT Class 12 · Ch 5 Exercise 5.7 · Q17
NCERT Class 12 Maths · Chapter 5 Continuity And Differentiability · Exercise 5.7 Question 17
If y=\(\operatorname{atan}^{2}{\left(x \right)}\), show (x²+1)²y″+2x(x²+1)y′=2.
💡 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: (x²+1)²y″+2x(x²+1)y′=2
- First derivative: y′=\(\frac{2 \operatorname{atan}{\left(x \right)}}{x^{2} + 1}\).
- Second derivative: y″=\(\frac{2 \left(- 2 x \operatorname{atan}{\left(x \right)} + 1\right)}{\left(x^{2} + 1\right)^{2}}\).
- Substitution into the indicated left-hand combination and simplification gives \(2\).
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