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The product rule differentiates a product of two functions: if y = uv then dy/dx = u(dv/dx) + v(du/dx). It is essential for differentiating expressions like x² sin x or eˣ ln x. 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
For a product uv, the derivative is u times the derivative of v, plus v times the derivative of u. Write u, v and both derivatives down separately before assembling — the errors come from doing it in your head.
Before you start
Best tackled after basic differentiation. You meet it in Pure 3. Expect to use it again in the quotient rule and harder calculus.
What you learn
This lesson builds from basic products, through products that also need the chain rule, products with roots, applications to gradients and tangents, and harder factorising. When one factor is itself a composite, you need the chain rule to differentiate it. When a factor is a root, write it as a power so you can differentiate it. The marks at the top end come from a clean factorisation. The course works through the product rule, product rule with the chain rule, products with roots, applying the product rule, harder products and products 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
Product Rule is a Differentiation topic in the A-level syllabus, covered here at the second year of A-level. There are 6 teaching sections and 6 fully worked examples, plus 6 sets of check questions. It sits alongside Quotient Rule, Reciprocal Trig and Second Derivatives & Stationary Points in the same strand. For unlimited practice, the Differentiation revision engine builds new questions on demand and records your accuracy.
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