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0606/11 Oct/Nov 2025, Question 7: The Product and Quotient Rules

Cambridge IGCSE Additional Mathematics 0606 · Paper 11 (Non-calculator) · Non-calculator · 7 marks

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The question, in short

Differentiate a quotient of a trigonometric sum and an exponential, then evaluate an integral involving a squared tangent.

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

Part (a) · 4 marks

Use the quotient rule on (sin x + cos x) divided by e^(1 − 3x) to obtain the derivative.

  1. 1Quotient rule with u = sin x + cos x, v = e^(1 − 3x)
  2. 2du/dx = cos x − sin x
  3. 3dv/dx = −3e^(1 − 3x)
  4. 4dy/dx = [e^(1 − 3x)(cos x − sin x) − (sin x + cos x)(−3e^(1 − 3x))]/(e^(1 − 3x))²
  5. 5This simplifies to (4 cos x + 2 sin x)e^(3x − 1)

Answer[e^(1 − 3x)(cos x − sin x) + 3e^(1 − 3x)(sin x + cos x)]/(e^(1 − 3x))²

Part (b) · 3 marks

Integrate 1 + tan²3x with respect to x, using a trigonometric identity.

  1. 11 + tan²3x = sec²3x
  2. 2∫ sec²3x dx = (1/3) tan 3x + c

Answer(1/3) tan 3x + c

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Also searched as: 0606/11/O/N/25 · 0606_w25_qp_11 · 0606 w25 11 · question 7.
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