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
Differentiate $y = (3x^2 - 1)^5$ .
Level 2 · 2 marksTry it
2
Differentiate $y = (2x + 5)^4$ .
Level 2 · 2 marksTry it
3
Differentiate $y = (5x - 2)^{3}$ . (2 marks)
Level 2 · 2 marksTry it
4
(a) Differentiate the following with respect to $x$ .

(i) $\ln(3x^2 + 5)$

(ii) $x\cos 4x$

(5 marks)
(b) Find $\displaystyle\int \sin 3x\,dx$ .

(2 marks)
(c) The gradient of a curve is given by $\dfrac{dy}{dx} = 4e^{2x}$ and the curve passes through the point $(0, 5)$ .

Find the equation of the curve.

(2 marks)
Level 2 · 9 marksTry it
5
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

11 more questions on the chain rule

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