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

✅ Step-by-Step Solution

1. Work on R.
2. Product rule: differentiate each variable factor once, keeping the other factors unchanged. Here \(\frac{d}{d x} \left(x + 3\right)^{2} \left(x + 4\right)^{3} \left(x + 5\right)^{4}\) = \(4 \left(x + 3\right)^{2} \left(x + 4\right)^{3} \left(x + 5\right)^{3} + 3 \left(x + 3\right)^{2} \left(x + 4\right)^{2} \left(x + 5\right)^{4} + \left(x + 4\right)^{3} \left(x + 5\right)^{4} \left(2 x + 6\right)\).
3. Combining the terms gives y′ = \(\left(x + 3\right) \left(x + 4\right)^{2} \left(x + 5\right)^{3} \left(9 x^{2} + 70 x + 133\right)\).