4PM1/01 Nov 2021, Question 4: 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 ÷ √(x² − 9) for |x| > 3 and show the result equals the given fraction with denominator √((x² − 9)³).
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Solution · 5 marks
- 1Quotient rule: dy/dx = [2cos 2x (x² − 9)^(1/2) − (1/2)(2x)sin 2x (x² − 9)^(−1/2)]/(x² − 9)
- 2Multiply numerator and denominator by (x² − 9)^(1/2)
- 3dy/dx = [2(x² − 9)cos 2x − x sin 2x]/(x² − 9)^(3/2)
- 4= [2(x² − 9)cos 2x − x sin 2x]/√((x² − 9)³)
Answerdy/dx = [2(x² − 9)cos 2x − x sin 2x]/√((x² − 9)³) shown
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