Lesson G4

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

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

In partnership with Revision Ninja

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

Host it live on the board and students join with a game code on their own devices, or revise alone with Free Play. The answers are revealed in the game.

Host this setFree Play

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 differentiation rule is required to differentiate y = x / (x + 1)?

    • Quotient rule
    • Chain rule
    • Product rule
    • Power rule

  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 increasing at 0.2 cm/s. What is dV/dt when r = 3 cm?

    • 7.2π cm³/s
    • 14.4π cm³/s
    • 1.2π cm³/s
    • 3.6π cm³/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))

All AQA Maths quizzes