Lesson G2

G2 Differentiating powers, exponentials, logarithms and trigonometry Quiz: AQA Maths, Unit 7

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson G2, Differentiating powers, exponentials, logarithms and trigonometry: 20 multiple choice questions for the AQA Maths (7357), Unit 7: Differentiation, written with Revision Ninja.

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The 20 questions

  1. What is the derivative of x^n for rational n?

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

  2. What is the derivative of e^(kx)?

    • e^(kx) / k
    • k e^(kx)
    • k x e^(kx - 1)
    • e^(kx)

  3. What is the derivative of ln x for x > 0?

    • 1/x^2
    • x
    • ln x
    • 1/x

  4. What is the derivative of sin kx?

    • k sin kx
    • k cos kx
    • cos kx
    • -k cos kx

  5. What is the derivative of cos x?

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

  6. What is the derivative of tan x?

    • sec^2 x
    • cos^2 x
    • sec x tan x
    • cosec^2 x

  7. What is the derivative of a^x for a > 0?

    • a^x / ln a
    • x a^(x - 1)
    • a^x ln x
    • a^x ln a

  8. Differentiate 3x^4 - 2x^2 + 5.

    • 12x^3 - 4x
    • 12x^3 - 2x
    • 3x^3 - 4x
    • 12x^4 - 4x^2

  9. Differentiate 5e^(2x).

    • 10x e^(2x)
    • 10e^(2x)
    • 2e^(2x)
    • 5e^(2x)

  10. Differentiate 2 ln x + 3x^2.

    • 2/x + 6x
    • 2/x + 3x
    • 1/x + 6x
    • 2 ln x + 6x

  11. Differentiate sin 3x.

    • -3 cos 3x
    • cos 3x
    • 3 cos 3x
    • 3 sin 3x

  12. Find the gradient of y = 4 cos 2x at x = pi/4.

    • 0
    • 8
    • -8
    • -4

  13. Find dy/dx for y = 3x^(-2) + sqrt(x).

    • -3/x^3 + 1/(2 sqrt(x))
    • -6/x^3 + sqrt(x)/2
    • -6/x^3 + 1/(2 sqrt(x))
    • 6/x^3 + 1/(2 sqrt(x))

  14. Find the gradient of y = x^3 - 3 ln x at x = 1.

    • 3
    • 0
    • 1
    • -3

  15. Find the derivative of f(x) = e^x + 4 sin x.

    • e^x - 4 cos x
    • e^x + 4 sin x
    • x e^(x - 1) + 4 cos x
    • e^x + 4 cos x

  16. A curve is y = 2x^(3/2). What is its gradient at x = 4?

    • 6
    • 8
    • 3
    • 12

  17. For which x is the gradient of y = e^(2x) equal to 4?

    • x = (1/2) ln 2
    • x = 2 ln 2
    • x = ln 4
    • x = (ln 2)/4

  18. Differentiate y = ln(x^2) after applying a log law first.

    • x^2 / 2
    • 2 ln x / x
    • 1/x
    • 2/x

  19. Which standard limit is used to show d/dx(sin x) = cos x from first principles?

    • lim as h tends to 0 of tan h = 1
    • lim as h tends to 0 of (sin h)/h = 1
    • lim as h tends to 0 of (1 - cos h)/h = 1
    • lim as h tends to 0 of h/(sin h) = 0

  20. Find f'(0) for f(x) = e^(3x) + 2 cos x.

    • 5
    • 2
    • 0
    • 3

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