NCERT Class 12 · Ch 5 Exercise 5.7 · Q2
NCERT Class 12 Maths · Chapter 5 Continuity And Differentiability · Exercise 5.7 Question 2
Find the second derivative of \(x^{20}\) 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: \(380 x^{18}\)
- Work on R.
- Power and chain rules: \(\frac{d}{d x} x^{20}\) = \(20 x^{19}\) × \(1\) = \(20 x^{19}\).
- Differentiate the first derivative \(20 x^{19}\) again.
- Power and chain rules: \(\frac{d}{d x} x^{19}\) = \(19 x^{18}\) × \(1\) = \(19 x^{18}\).
- Carry the constant factor: \(\frac{d}{d x} 20 x^{19}\) = \(380 x^{18}\).
- Combining the terms gives y″ = \(380 x^{18}\).
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