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 $y = x\sqrt{2x + 1}$ , giving your answer as a single fraction.
Level 3 · 3 marksTry it
2
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
3
The curve $C$ has equation $y = x\ln x$ , $\; x > 0$ .
(a) Find $\dfrac{dy}{dx}$ . (2 marks)
(b) Hence find the exact $x$ -coordinate of the stationary point of $C$ . (2 marks)
Level 3 · 4 marksTry it
4
Find an equation of the tangent to the curve $y = x\mathrm{e}^{x}$ at the point where $x = 1$ , giving your answer in terms of $\mathrm{e}$ . (4 marks)
Level 3 · 4 marksTry it
5
Differentiate $y = (2x + 1)^{3}(x - 2)$ , giving your answer in fully factorised form. (4 marks)
Level 3 · 4 marksTry it

8 more questions on the product rule

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