4PM1/01 Jun 2023, Question 2: The Product and Quotient Rules
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 1 · Calculator · 5 marks
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The question, in short
Differentiate y = (sin 2x)√(3 + 2x) and show it equals (sin 2x + (A + Bx)cos 2x)/√(3 + 2x), finding integers A and B.
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Solution · 5 marks
- 1Product rule with u = sin 2x, v = (3 + 2x)^(1/2)
- 2dy/dx = sin 2x × (1/2) × 2(3 + 2x)^(−1/2) + (3 + 2x)^(1/2) × 2cos 2x
- 3= sin 2x/√(3 + 2x) + 2√(3 + 2x) cos 2x
- 4= (sin 2x + 2(3 + 2x)cos 2x)/√(3 + 2x)
- 5= (sin 2x + (6 + 4x)cos 2x)/√(3 + 2x), so A = 6, B = 4
Answerdy/dx = (sin 2x + (6 + 4x)cos 2x)/√(3 + 2x), so A = 6 and B = 4
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