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Connected rates of change use the chain rule to link the rates at which two or more quantities vary with time, combining known derivatives through dy/dt = dy/dx × dx/dt to find an unknown rate. It appears across A-Level and iAL Pure Maths with the major exam boards. Learn it free on eClassroom through guided worked examples and instantly-marked exam-style questions.
How you do it
Write down every rate you are given and the one you want, as derivatives. Link them with the chain rule, cancelling the middle variable. If a rate is missing, differentiate a formula connecting the quantities to supply it.
Before you start
You need the chain rule before this makes sense. It leads on to modelling questions in Pure 4.
What you learn
When two quantities both change with time, their rates are linked by the chain rule. To connect two rates, write down the relationship between the quantities, differentiate it, and join the pieces with the chain rule. The classic Pure 4 vessel is an inverted cone. Some vessels come with the volume already written as a function of the depth. The course works through connecting two rates, differentiating the formula, the cone: reducing to one variable, vessels with a given volume formula, rates proportional to a quantity and chaining several rates. 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
Connected Rates of Change is a Differentiation topic in the A-level syllabus, covered here 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. Students often pair it with 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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