Product rule

Students will learn what the product rule is, why we need it, why it's true, and how to use it. First, students will see a proof of the product rule from first principles, as seen here. Then students will see a proof using the chain rule, as shown here. Before attempting this section, students should know the the power rule, the derivatives of \(\sin x\), \(\cos x\), \(\tan x\), \(\ln(x)\), and \(e^x\).