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The quotient rule differentiates a fraction of two functions: if y = u/v then dy/dx = (v u′ − u v′)/v². It is used whenever one function is divided by another, such as (sin x)/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 u over v, the derivative is v times u prime minus u times v prime, all over v squared. The order in the numerator matters because of the subtraction, so write it down before substituting. Sometimes rewriting as a product is quicker.
Before you start
Best tackled after the product and chain rules. This sits in Pure 3. Keep it sharp for differentiating trigonometric and rational functions.
What you learn
and quotients with trig, exponentials and logs. Getting the subtraction the wrong way round flips the sign. The course works through the quotient rule, quadratic numerators and denominators, quotient rule with the chain rule, applying the quotient rule, quotient rule, or rewrite? 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
Quotient 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. Nearby topics in the same strand are Reciprocal Trig, Second Derivatives & Stationary Points, Standard Functions and Tangents & Normals. You can drill this strand further on the Differentiation revision engine, with your accuracy saved to your skill tree.
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