NCERT Class 12 Maths · Chapter 5 Continuity And Differentiability · Miscellaneous Exercise Question 8

✅ Step-by-Step Solution

1. Work on R.
2. Differentiate the outer function and multiply by the inner derivative: \(\frac{\partial}{\partial x} \cos{\left(a \cos{\left(x \right)} + b \sin{\left(x \right)} \right)}\) = \(- \left(- a \sin{\left(x \right)} + b \cos{\left(x \right)}\right) \sin{\left(a \cos{\left(x \right)} + b \sin{\left(x \right)} \right)}\).
3. Combining the terms gives y′ = \(\left(a \sin{\left(x \right)} - b \cos{\left(x \right)}\right) \sin{\left(a \cos{\left(x \right)} + b \sin{\left(x \right)} \right)}\).