A-level · Differentiation

The quotient ruleExam-style questions

Differentiating one function divided by another. Why differentiating the top and bottom separately fails; where the rule comes from; the quotient rule (u'v − uv') ÷ v² with the order that matters; simplifying the top and leaving the bottom alone; stationary points and increasing intervals from the top's sign; and when rewriting is quicker than the rule.

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27 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAllLevel 2Level 3Level 4Level 5
  1. 1
    Differentiate y=xx+1y = \dfrac{x}{x + 1}.
    Level 2 · 2 marksTry it
  2. 2
    Differentiate y=3x−1x+2y = \dfrac{3x - 1}{x + 2}, simplifying your answer. (3 marks)
    Level 2 · 3 marksTry it