4PM1/02 Jun 2024, Question 5: The Product and Quotient Rules
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2 · Calculator · 7 marks
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The question, in short
For y = e^(2x)(x² − 5x), find the first and second derivatives and use them to show that 2e^(2x) equals d²y/dx² − 4 dy/dx + 4y.
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Solution · 7 marks
- 1dy/dx = 2e^(2x)(x² − 5x) + e^(2x)(2x − 5) = 2y + e^(2x)(2x − 5)
- 2So e^(2x)(2x − 5) = dy/dx − 2y
- 3d²y/dx² = 2 dy/dx + 2e^(2x)(2x − 5) + 2e^(2x)
- 4d²y/dx² = 2 dy/dx + 2(dy/dx − 2y) + 2e^(2x)
- 5Rearrange: 2e^(2x) = d²y/dx² − 4 dy/dx + 4y
Answer2e^(2x) = d²y/dx² − 4 dy/dx + 4y shown
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