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

DifficultyAll Level 2 Level 3 Level 4 Level 5

1
Differentiate $y = \dfrac{x}{\sqrt{x + 4}}$ .
Level 3 · 3 marksTry it
2
In this question you must show all stages of your working.

Solutions relying on calculator technology are not acceptable.

A curve has equation

$y = \dfrac{3x - 5}{(x - 1)^2} \qquad x \neq 1,\ x \in \mathbb{R}$

Use calculus to find the range of values of $x$ for which $y$ is increasing.

(6 marks)
Level 3 · 6 marksTry it
3
A curve has equation $y = \dfrac{x^2 + 1}{x - 1}$ . Find the gradient of the curve at the point where $x = 2$ .
Level 3 · 3 marksTry it
4
The curve $C$ has equation $y = \dfrac{2x + 1}{x - 3}$ .

Verify that the point $(4, 9)$ lies on $C$ , and find the gradient of $C$ there. (3 marks)
Level 3 · 3 marksTry it
5
Differentiate $y = \dfrac{\sin x}{x}$ , $\; x \neq 0$ . (3 marks)
Level 3 · 3 marksTry it

9 more questions on the quotient rule

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