NCERT Class 12 · Ch 5 Exercise 5.7 · Q4
NCERT Class 12 Maths · Chapter 5 Continuity And Differentiability · Exercise 5.7 Question 4
Find the second derivative of \(\log{\left(x \right)}\) with respect to x; for x>0.
💡 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: \(- \frac{1}{x^{2}}\)
- Work for x>0.
- Differentiate the outer function and multiply by the inner derivative: \(\frac{d}{d x} \log{\left(x \right)}\) = \(\frac{1}{x}\).
- Differentiate the first derivative \(\frac{1}{x}\) again.
- Power and chain rules: \(\frac{d}{d x} \frac{1}{x}\) = \(- \frac{1}{x^{2}}\) × \(1\) = \(- \frac{1}{x^{2}}\).
- Combining the terms gives y″ = \(- \frac{1}{x^{2}}\).
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