4PM1/02R Jun 2025, Question 8: The Product and Quotient Rules
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2R · Calculator · 5 marks
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The question, in short
Differentiate y = e^(3x)(9x + 2)^(1/3) using calculus and evaluate the gradient at x = 1, giving the answer to 3 significant figures.
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Solution · 5 marks
- 1Product rule: dy/dx = 3e^(3x)(9x + 2)^(1/3) + e^(3x) × (1/3)(9)(9x + 2)^(−2/3)
- 2= 3e^(3x)(9x + 2)^(1/3) + 3e^(3x)(9x + 2)^(−2/3)
- 3At x = 1: 3e³(11)^(1/3) + 3e³(11)^(−2/3)
- 4= 134.0… + 12.18… = 146 (3 s.f.)
Answer146
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