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
    It is given that f(x)=2x3+5xf(x) = 2x^3 + 5x.
    (a) Use differentiation from first principles to show that f′(x)=6x2+5f'(x) = 6x^2 + 5.

    (5 marks)
    (b) A curve passes through the point (−1,4)(-1, 4), and its gradient at the point (x,y)(x, y) is 6x2+56x^2 + 5.

    Find the equation of the curve.

    (3 marks)
    Level 4 · 8 marksTry it