alleryd/dx [(x² + 1)(x + 1)] using product rule equals:
A(2x + 1)(x + 1)
B(2x)(x² + 1) + (x² + 1)
C2x(x + 1) + (x² + 1)
D(x² + 1)(2x + 1)
Answer & Solution
Correct answer: C. 2x(x + 1) + (x² + 1)
1. Product rule: (uv)′ = u′v + uv′.
2. Let u = x² + 1 (u′ = 2x); v = x + 1 (v′ = 1).
3. (uv)′ = 2x · (x + 1) + (x² + 1) · 1 = 2x(x + 1) + (x² + 1).
4. Expanded: 2x² + 2x + x² + 1 = 3x² + 2x + 1.
_Source: syllabus Maths Ch 13 §13.4 Product Rule_
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