NCERT Class 12 Maths · Chapter 5 Continuity And Differentiability · Exercise 5.2 Question 4

✅ Step-by-Step Solution

1. Work where x>0 and tan(√x), sec(tan(√x)) are defined.
2. Differentiate the outer function and multiply by the inner derivative: \(\frac{d}{d x} \sec{\left(\tan{\left(\sqrt{x} \right)} \right)}\) = \(\frac{\left(\tan^{2}{\left(\sqrt{x} \right)} + 1\right) \tan{\left(\tan{\left(\sqrt{x} \right)} \right)} \sec{\left(\tan{\left(\sqrt{x} \right)} \right)}}{2 \sqrt{x}}\).
3. Combining the terms gives y′ = \(\frac{\tan{\left(\tan{\left(\sqrt{x} \right)} \right)} \sec{\left(\tan{\left(\sqrt{x} \right)} \right)}}{2 \sqrt{x} \cos^{2}{\left(\sqrt{x} \right)}}\).