A-level · Differentiation

Differentiation from first principlesExam-style questions

The definition every differentiation rule is built on. What "the gradient at a point" means, as the limit of chords; the definition f'(x) as a limit; writing out f(x + h) correctly; cancelling h before letting it shrink; setting out the proof the way the marks are given; and finding the gradient at one point from first principles.

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

DifficultyAllLevel 2Level 3Level 4Level 5
  1. 1
    Differentiate f(x)=xf(x) = \sqrt{x} from first principles.
    Level 5 · 4 marksTry it
  2. 2
    Differentiate f(x)=1xf(x) = \dfrac{1}{x} from first principles.
    Level 5 · 4 marksTry it