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The chain rule differentiates composite (function-of-a-function) expressions: dy/dx = dy/du × du/dx. It is essential for differentiating things like (3x + 1)⁵, e^(x²) and sin(2x). 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
Identify the inside function and the outside function. Differentiate the outside, leaving the inside alone, then multiply by the derivative of the inside. Written as dy/dx equals dy/du times du/dx, it is a chain of substitutions.
Before you start
Before starting, revisit basic differentiation and composite functions. Getting it right here pays off in implicit and parametric differentiation.
What you learn
Don’t forget to multiply by the derivative of the inside. The chain rule extends to the standard functions. The course works through powers of a bracket, the general chain rule, roots and reciprocals, applying the chain rule, the reciprocal relationship and chain rule with trig, exponentials and logs. 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
We teach Chain Rule as one of the Differentiation topics in our A-level course library, at the second year of A-level. The course is built from 6 concept sections, 6 worked examples and 6 check points before the exam-style set. Nearby topics in the same strand are Connected Rates of Change, Differentiation from First Principles, Implicit Differentiation, Increasing & Decreasing Functions and Parametric Differentiation. The Differentiation revision engine gives you as many extra questions as you want, tracked on your skill tree.
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