NCERT Class 12 Maths · Chapter 5 Continuity And Differentiability · Exercise 5.7 Question 10

✅ Step-by-Step Solution

1. Work for x>0.
2. Differentiate the outer function and multiply by the inner derivative: \(\frac{d}{d x} \sin{\left(\log{\left(x \right)} \right)}\) = \(\frac{\cos{\left(\log{\left(x \right)} \right)}}{x}\).
3. Differentiate the first derivative \(\frac{\cos{\left(\log{\left(x \right)} \right)}}{x}\) again.
4. Product rule: differentiate each variable factor once, keeping the other factors unchanged. Here \(\frac{d}{d x} \frac{\cos{\left(\log{\left(x \right)} \right)}}{x}\) = \(- \frac{\sin{\left(\log{\left(x \right)} \right)}}{x^{2}} - \frac{\cos{\left(\log{\left(x \right)} \right)}}{x^{2}}\).
5. Combining the terms gives y″ = \(- \frac{\sin{\left(\log{\left(x \right)} \right)} + \cos{\left(\log{\left(x \right)} \right)}}{x^{2}}\).