Derivatives

Derivatives measure how fast something is changing at a single instant. By the time you reach this topic you probably know the power rule, so it focuses on the two places where AP Calculus marks most often go missing. The first is the chain rule. When one function sits inside another, you differentiate the outside, keep the inside as it is, then multiply by the inside's derivative. That last multiplication is the step people drop. The same idea explains implicit differentiation: y depends on x, so every y term you differentiate picks up a dy/dx. The second page is about maxima and minima. Setting the derivative equal to zero only finds candidates. You still need to check whether the derivative changes sign there, and on a closed interval you must check the endpoints too. Work through both pages in order, write the inside function out before you start, and draw a quick sign chart for every critical point.