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Differentiation finds the gradient function dy/dx, the rate of change of a curve at any point. This topic covers differentiating xⁿ from the power rule, differentiating sums of terms and evaluating gradients. 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
Multiply by the power and reduce the power by one, term by term. Rewrite roots and reciprocals as powers first — root x becomes x to the half, and 1 over x squared becomes x to the minus 2 — so the rule applies. Constants differentiate to zero.
Before you start
Bring index laws and function notation with you. The same ideas return in tangents, normals and stationary points.
What you learn
At this stage there is no product or quotient rule — so expand a product and split a quotient into separate powers of x before differentiating. The course works through the power rule, negative & fractional indices, rewrite products & quotients first, the gradient at a point and the gradient equation. 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
Basic Differentiation is part of the Differentiation strand of our free A-level maths courses, studied in the AS year. There are 5 teaching sections and 5 fully worked examples, plus 5 sets of check questions. Nearby topics in the same strand are Chain Rule, Connected Rates of Change and Differentiation from First Principles. The Differentiation revision engine gives you as many extra questions as you want, tracked on your skill tree.
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