NCERT Class 12 · Ch 5 Exercise 5.7 · Q1
NCERT Class 12 Maths · Chapter 5 Continuity And Differentiability · Exercise 5.7 Question 1
Find the second derivative of \(x^{2} + 3 x + 2\) with respect to x; on R.
💡 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: \(2\)
- Work on R.
- Power and chain rules: \(\frac{d}{d x} x^{2}\) = \(2 x\) × \(1\) = \(2 x\).
- Carry the constant factor: \(\frac{d}{d x} 3 x\) = \(3\).
- Sum rule: \(\frac{d}{d x} \left(x^{2} + 3 x + 2\right)\) = \(2 x + 3\).
- Differentiate the first derivative \(2 x + 3\) again.
- Carry the constant factor: \(\frac{d}{d x} 2 x\) = \(2\).
- Sum rule: \(\frac{d}{d x} \left(2 x + 3\right)\) = \(2\).
- Combining the terms gives y″ = \(2\).
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