Rates of Change

This lesson covers connected rates of change, a key topic in A-Level Mathematics. Here we apply the chain rule to link rates at which different quantities change, enabling us to solve problems about expanding shapes, filling containers, and other dynamic real-world situations.

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The Chain Rule for Connected Rates

The chain rule states that if y is a function of u and u is a function of x, then:

dy/dx = (dy/du) × (du/dx)

This principle extends to rates of change with respect to time. If a quantity V depends on a radius r, and both change with time t, then:

dV/dt = (dV/dr) × (dr/dt)

This connects the rate of change of volume with the rate of change of radius.

Exam Tip: The chain rule for connected rates of change is one of the most commonly examined topics. Always identify the rate you want, the rate you know, and the link between the variables.

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Strategy for Connected Rates Problems