Product Rule Application

Calculus 1 · Axiom Academy

EXAMPLE Product Rule Application Differentiating exponential and polynomial products Find the derivative of y = x^2 e^x . This is a product of two functions, so we'll need the product rule (fg)' = f'g + fg' . Nice work. You applied the product rule to an exponential function. Here's what we learned: Exponential derivatives: the derivative of e^x is e^x itself — this special property makes exponential functions unique. Factoring strategy: when the same factor appears in both terms of the product rule result, factor it out for a cleaner answer. Simplification matters: the factored form e^x(x^2 + 2x) is more elegant and useful than the expanded form. Products involving e^x often simplify nicely because the exponential function is its own derivative.

This is the written version of the interactive lesson above. See the full Calculus 1 course.