Cambridge O Level Additional Mathematics · Syllabus 4037 · Calculus
Connected Rates of Change
What is Connected Rates of Change?
A technique for finding an unknown rate of change from a known one when two quantities are linked by a formula. If A depends on r and r depends on time, then the rate at which A changes with time is the product of the rate at which A changes with r and the rate at which r changes with time, written dA by dt equals dA by dr multiplied by dr by dt. The method is the chain rule applied with time as the underlying variable. Every rate carries units built from the two quantities involved, and a negative rate means the quantity is decreasing, so both units and signs form part of a complete answer.
This definition is part of the Calculus chapter in Cambridge O Level Additional Mathematics.