Whitman College: David Guichard's "Calculus, Chapter 3: Rules for Finding Derivatives, Section 3.3: The Product Rule"
Read Section 3.3 (pages 60 and 61). The naïve assumption is that the derivative of a product of two functions is the product of the derivatives of the two functions. This assumption is false. In this reading, you will see that the derivative of a product is slightly more complicated, but that it follows a definite rule, called the product rule.