NCERT Class 12 Maths · Chapter 5 Continuity And Differentiability · Exercise 5.7 Question 9

✅ Step-by-Step Solution

1. Work for x>1.
2. Differentiate the outer function and multiply by the inner derivative: \(\frac{d}{d x} \log{\left(\log{\left(x \right)} \right)}\) = \(\frac{1}{x \log{\left(x \right)}}\).
3. Differentiate the first derivative \(\frac{1}{x \log{\left(x \right)}}\) again.
4. Product rule: differentiate each variable factor once, keeping the other factors unchanged. Here \(\frac{d}{d x} \frac{1}{x \log{\left(x \right)}}\) = \(- \frac{1}{x^{2} \log{\left(x \right)}} - \frac{1}{x^{2} \log{\left(x \right)}^{2}}\).
5. Combining the terms gives y″ = \(- \frac{\log{\left(x \right)} + 1}{x^{2} \log{\left(x \right)}^{2}}\).