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4PM1/01R Jan 2020, Question 3: The Product and Quotient Rules

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 1R · Calculator · 6 marks

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The question, in short

Differentiate y = e^(2x)(x² + 1), then find the tangent line at x = 0 and express it as y = mx + c.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (a) · 3 marks

Find dy/dx of y = e^(2x)(x² + 1).

  1. 1Product rule with u = e^(2x), v = x² + 1
  2. 2u′ = 2e^(2x), v′ = 2x
  3. 3dy/dx = 2e^(2x)(x² + 1) + 2xe^(2x)

Answerdy/dx = 2e^(2x)(x² + 1) + 2xe^(2x)

Part (b) · 3 marks

Find the equation of the tangent line l at x = 0, giving it in y = mx + c form.

  1. 1At x = 0: dy/dx = 2(1)(1) + 0 = 2
  2. 2At x = 0: y = e⁰(0 + 1) = 1
  3. 3y − 1 = 2(x − 0), so y = 2x + 1

Answery = 2x + 1

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