Product Rule

AP Calculus · Axiom Academy

Differentiating products of functions When you need to differentiate the product of two functions, you can't just multiply the derivatives. Instead, you use the Product Rule: Let's understand where the product rule comes from. Using the limit definition: When we expand f(x+h)g(x+h) and subtract f(x)g(x), we get four terms. After careful algebra and limit-taking, the Product Rule emerges naturally. You've mastered the Product Rule! Next: The Quotient Rule—for dividing functions.

This is the written version of the interactive lesson above. See the full AP Calculus course.