NCERT Class 12 Maths · Chapter 5 Continuity And Differentiability · Miscellaneous Exercise Question 2

✅ Step-by-Step Solution

1. Work on R.
2. Power and chain rules: \(\frac{d}{d x} \cos^{6}{\left(x \right)}\) = \(6 \cos^{5}{\left(x \right)}\) × \(- \sin{\left(x \right)}\) = \(- 6 \sin{\left(x \right)} \cos^{5}{\left(x \right)}\).
3. Power and chain rules: \(\frac{d}{d x} \sin^{3}{\left(x \right)}\) = \(3 \sin^{2}{\left(x \right)}\) × \(\cos{\left(x \right)}\) = \(3 \sin^{2}{\left(x \right)} \cos{\left(x \right)}\).
4. Sum rule: \(\frac{d}{d x} \left(\sin^{3}{\left(x \right)} + \cos^{6}{\left(x \right)}\right)\) = \(3 \sin^{2}{\left(x \right)} \cos{\left(x \right)} - 6 \sin{\left(x \right)} \cos^{5}{\left(x \right)}\).
5. Combining the terms gives y′ = \(3 \left(\sin{\left(x \right)} - 2 \cos^{4}{\left(x \right)}\right) \sin{\left(x \right)} \cos{\left(x \right)}\).