Lesson G4

G4 Product, quotient and chain rules Quiz: AQA Maths, Unit 7

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson G4, Product, quotient and chain rules: 20 multiple choice questions for the AQA Maths (7357), Unit 7: Differentiation, written with Revision Ninja.

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The 20 questions

  1. State the product rule for y = uv.

    • dy/dx = du/dx x dv/dx
    • dy/dx = u du/dx + v dv/dx
    • dy/dx = u dv/dx + v du/dx
    • dy/dx = u dv/dx - v du/dx

  2. State the quotient rule for y = u/v.

    • dy/dx = (v du/dx - u dv/dx)/v
    • dy/dx = (v du/dx - u dv/dx)/v^2
    • dy/dx = (u dv/dx - v du/dx)/v^2
    • dy/dx = (du/dx)/(dv/dx)

  3. State the chain rule for y = f(g(x)).

    • dy/dx = f(g'(x))
    • dy/dx = f'(g(x)) + g'(x)
    • dy/dx = f'(x) x g'(x)
    • dy/dx = f'(g(x)) x g'(x)

  4. Differentiate x e^x.

    • e^x
    • e^x + x e^x
    • x e^x
    • e^x - x e^x

  5. Differentiate (2x + 1)^3 using the chain rule.

    • 6(2x + 1)^3
    • (2x + 1)^2
    • 6(2x + 1)^2
    • 3(2x + 1)^2

  6. Differentiate ln(x^2 + 1).

    • 2/(x^2 + 1)
    • x/(x^2 + 1)
    • 1/(x^2 + 1)
    • 2x/(x^2 + 1)

  7. Which rule is needed to differentiate y = x/(x + 1)?

    • The chain rule alone
    • The quotient rule
    • The product rule
    • Implicit differentiation

  8. Differentiate y = x sin x.

    • sin x - x cos x
    • cos x - x sin x
    • sin x + x cos x
    • x cos x

  9. Differentiate y = x^2/(x + 1) using the quotient rule.

    • 2x/(x + 1)^2
    • (2x^2 + 2x)/(x + 1)^2
    • (x^2 - 2x)/(x + 1)^2
    • (x^2 + 2x)/(x + 1)^2

  10. Differentiate y = sqrt(3x - 1).

    • 3/(2 sqrt(3x - 1))
    • (3x - 1)^(-1/2)
    • 1/(2 sqrt(3x - 1))
    • 3/sqrt(3x - 1)

  11. Differentiate y = e^(x^2).

    • e^(2x)
    • x^2 e^(x^2 - 1)
    • 2x e^(x^2)
    • 2 e^(x^2)

  12. Differentiate y = cos^2 x.

    • 2 cos x
    • 2 sin x cos x
    • -2 sin x cos x
    • -sin^2 x

  13. What is the gradient of y = x e^(-x) at x = 0?

    • -1
    • 1
    • 2
    • 0

  14. A cube has volume V = x^3. If dV/dt = 6 cm^3/s when x = 2, what is dx/dt?

    • 0.5 cm/s
    • 72 cm/s
    • 2 cm/s
    • 0.125 cm/s

  15. If dy/dx = 4 at x = 1 for a function with inverse, what is dx/dy at the corresponding point?

    • 1/4
    • -1/4
    • 4
    • 1

  16. Differentiate y = x^2 e^(3x).

    • 3x^2 e^(3x)
    • x(3x - 2) e^(3x)
    • x(3x + 2) e^(3x)
    • 2x e^(3x)

  17. Differentiate y = ln(sin x) for sin x > 0.

    • -cot x
    • tan x
    • cot x
    • 1/cos x

  18. Find dy/dx for y = (x + 1)/(x - 1) at x = 2.

    • -1/2
    • -2
    • 2
    • -4

  19. A sphere has radius growing at 0.2 cm/s. What is the rate of change of its volume when r = 3 cm, using V = (4/3) pi r^3?

    • 36 pi cm^3/s
    • 1.8 pi cm^3/s
    • 7.2 pi cm^3/s, about 22.6 cm^3/s
    • 0.6 pi cm^3/s

  20. Differentiate y = sqrt(x) e^x.

    • e^x (1 + 2x)/(2 sqrt(x))
    • sqrt(x) e^x + e^x
    • e^x (1 - 2x)/(2 sqrt(x))
    • e^x/(2 sqrt(x))

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