The derivative of a function represents the rate of change of one variable with respect to another at a given point. It is a slope and itself a function that varies across points. To find the derivative of a function f(x) at a point, we use the slope formula and take the limit as the change in x approaches 0. For example, the derivative of x^2 is 2x, meaning the slope or rate of change of x^2 is 2x at any point. There are various rules for finding derivatives, such as the power rule, sum and difference rules, product rule and quotient rule.