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0606/22 May/Jun 2026, Question 3: The Chain Rule

Cambridge IGCSE Additional Mathematics 0606 · Paper 22 (Calculator) · Calculator · 6 marks

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The question, in short

Obtain the derivative of a sum involving a square root and a cosine, then evaluate an indefinite integral of sec squared with a scaled angle.

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

Part (a) · 3 marks

Find dy/dx for y = √(x + 1) + cos(5x + 3).

  1. 1√(x + 1) = (x + 1)^(1/2), derivative (1/2)(x + 1)^(−1/2)
  2. 2d/dx cos(5x + 3) = −5 sin(5x + 3)
  3. 3dy/dx = (1/2)(x + 1)^(−1/2) − 5 sin(5x + 3)

Answerdy/dx = (1/2)(x + 1)^(−1/2) − 5 sin(5x + 3)

Part (b) · 3 marks

Work out the indefinite integral of sec²(x/3) with respect to x.

  1. 1d/dx tan(x/3) = (1/3) sec²(x/3)
  2. 2So ∫ sec²(x/3) dx = 3 tan(x/3) + c

Answer3 tan(x/3) + c

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Also searched as: 0606/22/M/J/26 · 0606_s26_qp_22 · 0606 s26 22 · question 3.
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