Math basics › More calculus

Related rates

Everything is a function of time

Write the relationship between the quantities first, then differentiate the whole thing with respect to t. Every variable picks up a d/dt by the chain rule.

Substitute numbers last

Put the given values in only after differentiating. A quantity that is changing cannot be replaced by a number while it is still inside the derivative.

Draw it and label it

Almost every related rates problem is a triangle, a circle or a cone. The picture tells you which formula relates the quantities.