top of page
Differentiation from first principles derives the gradient function from the limit definition, f′(x) = lim(h→0)[f(x+h) − f(x)]/h, showing where the rules of differentiation come from. It's a key topic in A-Level and International A-Level (iAL) Pure Mathematics. This free interactive course teaches the method with worked examples and gives instant-feedback practice questions to lock it in.
How you do it
Write the gradient of the chord as f of x plus h minus f of x, all over h. Expand the numerator, cancel the h that divides through every term, then let h tend to zero in what is left. Cancelling before taking the limit is the step that makes it work.
Before you start
Best tackled after limits and algebraic expansion. Keep it sharp for understanding where the rules come from.
What you learn
The course works through the gradient of a chord, from chord to tangent: the limit and A reciprocal term, and the gradient at a point. Every section has instant-feedback practice questions matched to Edexcel International A-Level and 9MA0 Pure, and the course finishes with full exam-style questions you mark yourself.
Related Topics
In our A-level maths courses, Differentiation from First Principles belongs to Differentiation and is met in the AS year. The course is built from 5 concept sections, 5 worked examples and 5 check points before the exam-style set. Nearby topics in the same strand are Implicit Differentiation, Increasing & Decreasing Functions and Parametric Differentiation. Endless extra practice on this strand is available on the Differentiation revision engine, which generates a fresh question each time.
Still need help with a topic?
bottom of page