A-level · Differentiation

The chain ruleExam-style questions

Differentiating one function inside another. Spotting the inside and the outside; the chain rule dy/dx = (dy/du)(du/dx) and why the rates multiply; the working version for brackets, roots and reciprocals; using it for gradients, tangents and stationary points; and the reciprocal connection dy/dx = 1 ÷ dx/dy.

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

DifficultyAll Level 2 Level 3

1
A curve is given by $x = y^3 + y$ . Find $\dfrac{dy}{dx}$ in terms of $y$ , and its value at the point where $y = 1$ .
Level 3 · 3 marksTry it
2
The curve $C$ has equation $y = (x^{2} - 4x)^{3}$ .

Find the $x$ -coordinates of the stationary points of $C$ . (4 marks)
Level 3 · 4 marksTry it
3
Differentiate $y = \dfrac{1}{(4 - 3x)^{2}}$ . (3 marks)
Level 3 · 3 marksTry it
4
Differentiate $y = \sqrt{1 + \sqrt{x}}$ .
Level 3 · 3 marksTry it
5
Given $y = \sqrt{x^{2} + 9}$ :
(a) find $\dfrac{dy}{dx}$ ; (3 marks)
(b) evaluate the gradient at $x = 4$ . (1 mark)
Level 3 · 4 marksTry it

7 more questions on the chain rule

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