AP Calculus AB and BC glossary
Related rate
A related rate is the rate of change of one quantity expressed in terms of the rate of change of another that it depends on. These problems link the quantities with an equation, then differentiate both sides with respect to time.
The order that keeps these problems honest is: write the geometric relationship first, differentiate with respect to time second, and substitute the given numerical values last.
The mistake
Substituting the numbers before differentiating. Doing so turns a changing quantity into a constant, whose derivative is zero, and the problem collapses.
Appears in: Unit 4: Contextual Applications