AP Calculus AB and BC glossary
Product rule
The product rule differentiates a product of two functions: multiply the first by the derivative of the second, then add the second times the derivative of the first. The derivative of a product is never the product of the derivatives.
The rule is needed only when both factors contain the variable. If one factor is a constant, the constant multiple rule applies and the work is much shorter.
The mistake
Writing the derivative of a product as . Testing it on shows the error immediately: the correct answer is , not 1.
The product rule explains a result that puzzles most economics students. Total revenue is price times quantity, and when price itself depends on quantity the derivative picks up a second term, so marginal revenue is the price plus a negative correction rather than just the price: marginal revenue.
Appears in: Unit 2: Defining the Derivative