NCERT Class 12 Maths · Chapter 5 Continuity And Differentiability · Exercise 5.5 Question 1

✅ Step-by-Step Solution

1. Work on R.
2. Product rule: differentiate each variable factor once, keeping the other factors unchanged. Here \(\frac{d}{d x} \cos{\left(x \right)} \cos{\left(2 x \right)} \cos{\left(3 x \right)}\) = \(- \sin{\left(x \right)} \cos{\left(2 x \right)} \cos{\left(3 x \right)} - 2 \sin{\left(2 x \right)} \cos{\left(x \right)} \cos{\left(3 x \right)} - 3 \sin{\left(3 x \right)} \cos{\left(x \right)} \cos{\left(2 x \right)}\).
3. Combining the terms gives y′ = \(- \frac{\sin{\left(2 x \right)} + 2 \sin{\left(4 x \right)} + 3 \sin{\left(6 x \right)}}{2}\).