2.8.2 Derivation of the Product Rule, Algebraically - Analytical Geometry and Calculus I

In this video, we derive the product rule algebraically, by adding and subtracting the appropriate terms in the numerator of the expression for the limit definition of the derivative of f(x)g(x).
We point out that the limit laws and the derivative rules are different from each other, and that can initially be a little confusing. Just keep in mind that the derivative rules are rules for calculating slope while the limit laws tell us what the functions approach as x approaches a particular x-value.