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

✅ Step-by-Step Solution

1. Work for −2<x<2.
2. Product rule: differentiate each variable factor once, keeping the other factors unchanged. Here \(\frac{d}{d x} \frac{\operatorname{acos}{\left(\frac{x}{2} \right)}}{\sqrt{2 x + 7}}\) = \(- \frac{\operatorname{acos}{\left(\frac{x}{2} \right)}}{\left(2 x + 7\right)^{\frac{3}{2}}} - \frac{1}{2 \sqrt{1 - \frac{x^{2}}{4}} \sqrt{2 x + 7}}\).
3. Combining the terms gives y′ = \(- \frac{\frac{\operatorname{acos}{\left(\frac{x}{2} \right)}}{2 x + 7} + \frac{1}{2 \sqrt{1 - \frac{x^{2}}{4}}}}{\sqrt{2 x + 7}}\).