A-level · Differentiation

Differentiating exponentials and logarithmsExam-style questions

The functions whose rate of change is proportional to their size. Why the gradient of any exponential is its height times a constant; the base e, which makes that constant exactly 1; e^(kx) with the chain rule; other bases and their factor of ln a; the derivative of ln x and of ln of anything; and exponentials and logs with the product and quotient rules.

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

DifficultyAllLevel 2Level 3Level 4Level 5
  1. 1
    Differentiate y=ln⁡(x3)y = \ln(x^{3}), simplifying your answer. (2 marks)
    Level 2 · 2 marksTry it
  2. 2
    Differentiate y=e3xy = e^{3x}.
    Level 2 · 2 marksTry it
  3. 3
    Differentiate y=e5x+e−2xy = \mathrm{e}^{5x} + \mathrm{e}^{-2x}. (2 marks)
    Level 2 · 2 marksTry it
  4. 4
    A curve has equation y=6e−2xy = 6e^{-2x}

    Find the gradient of the curve at the point where y=15y = 15

    (3 marks)
    Level 2 · 3 marksTry it
  5. 5
    Differentiate y=ln⁡(3x2+1)y = \ln(3x^2 + 1).
    Level 2 · 2 marksTry it

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