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0580/43 Oct/Nov 2025, Question 20: Differentiating Polynomials

Cambridge IGCSE Mathematics 0580 · Paper 43 (Extended) · Calculator · 4 marks

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The question, in short

For the curve y = x³ + 3x² − 13x, differentiate it and then work out the slope at x = 3.

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

Part (a) · 2 marks

Differentiate the given cubic expression with respect to x.

  1. 1Differentiate each term: multiply by the power, then lower the power by 1.
  2. 2x³ → 3x², 3x² → 6x, −13x → −13
  3. 3dy/dx = 3x² + 6x − 13

Answer3x² + 6x − 13

Part (b) · 2 marks

Evaluate the derivative at x = 3 to obtain the curve's gradient there.

  1. 1The gradient is the value of dy/dx
  2. 2x³ → 3x², 3x² → 6x, −13x → −13
  3. 3dy/dx = 3x² + 6x − 13
  4. 4At x = 3: 3(3)² + 6(3) − 13 = 27 + 18 − 13 = 32

Answer32

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Also searched as: 0580/43/O/N/25 · 0580_w25_qp_43 · 0580 w25 43 · question 20.
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