JAMB 2011 Mathematics · Question 28

The derivatives of (2x + 1)(3x + 1) is

Options

A.12x + 1
B.6x + 5
C.6x + 1
D.12x + 5

Answer: D. 12x + 5

Explanation written with AI and checked against the answer key

Analyze the question: We need the derivative of y = (2x + 1)(3x + 1). Concept: You can either expand first and then differentiate, or use the product rule: d/dx(uv) = u'v + uv'. Solution: Expand first: (2x + 1)(3x + 1) = 6x² + 2x + 3x + 1 = 6x² + 5x + 1 Differentiate term by term: dy/dx = 12x + 5 Check with the product rule: u = 2x + 1, so u' = 2 v = 3x + 1, so v' = 3 dy/dx = u'v + uv' = 2(3x + 1) + 3(2x + 1) = 6x + 2 + 6x + 3 = 12x + 5 Answer: D. 12x + 5 Tip: When both factors are linear, expanding first is usually quicker and less error-prone. Use the product rule as a cross-check. Remember that the power rule says d/dx(axⁿ) = naxⁿ⁻¹, so 6x² becomes 12x and 5x becomes 5.

AI can make mistakes. Report anything that looks wrong.