0606/13 Oct/Nov 2025, Question 2: The Product and Quotient Rules
Cambridge IGCSE Additional Mathematics 0606 · Paper 13 (Non-calculator) · Non-calculator · 3 marks
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The question, in short
Find the derivative, with respect to x, of the product x² times e raised to the power 3x.
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Solution · 3 marks
- 1Product rule: d/dx(uv) = u′v + uv′ with u = x², v = e^(3x)
- 2u′ = 2x, v′ = 3e^(3x)
- 3dy/dx = 2xe^(3x) + 3x²e^(3x)
Answer2xe^(3x) + 3x²e^(3x)
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