A-level · Differentiation

The product ruleExam-style questions

Differentiating two functions multiplied together. Why multiplying the two derivatives fails; the growing rectangle behind the rule; the product rule u'v + uv' and how to set it out; a bracket or a root as one factor, with the chain rule inside; factorising the answer; and finding the stationary points of a product from its factors.

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

DifficultyAll Level 2 Level 3 Level 4 Level 5

1
Differentiate $y = (x + 1)(x - 3)^4$ , giving your answer in factorised form.
Level 2 · 3 marksTry it
2
Differentiate $y = x^2(2x + 1)^3$ , giving your answer in fully factorised form.
Level 2 · 3 marksTry it
3
Differentiate $(x^2 + 4x - 1)e^{-x}$ with respect to $x$ , giving your answer in the form $e^{-x}(ax^2 + bx + c)$ , where $a$ , $b$ and $c$ are integers to be determined.

(3 marks)
Level 2 · 3 marksTry it
4
Differentiate $y = x\sqrt{2x + 1}$ , giving your answer as a single fraction.
Level 3 · 3 marksTry it
5
The curve $C$ has equation $y = x^{2}\mathrm{e}^{x}$ .

Find the $x$ -coordinates of the stationary points of $C$ . (4 marks)
Level 3 · 4 marksTry it

22 more questions on the product rule

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