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0606/12 Oct/Nov 2025, Question 12: The Product and Quotient Rules

Cambridge IGCSE Additional Mathematics 0606 · Paper 12 (Non-calculator) · Non-calculator · 6 marks

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The question, in short

For the curve y = e^(x²)/(x − 2) with x < 2, find the gradient at x = 0 and, given y increases at 0.5 units per second there, find the rate of change of x.

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Part (a) · 4 marks

Differentiate y = e^(x²)/(x − 2) and evaluate dy/dx at x = 0.

  1. 1Quotient rule: u = e^(x²), u′ = 2xe^(x²); v = x − 2, v′ = 1
  2. 2dy/dx = [(x − 2)·2xe^(x²) − e^(x²)]/(x − 2)²
  3. 3At x = 0: [(−2)(0) − 1]/(−2)² = −1/4

Answer−1/4

Part (b) · 2 marks

Using the gradient at x = 0 and dy/dt = 0.5, find dx/dt.

  1. 1dy/dt = (dy/dx) × (dx/dt)
  2. 20.5 = (−1/4) × dx/dt
  3. 3dx/dt = −2

Answer−2 (x is decreasing at 2 units per second)

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Also searched as: 0606/12/O/N/25 · 0606_w25_qp_12 · 0606 w25 12 · question 12.
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