The Derivative as a Function

A derivative quantifies how a function changes in response to variations in its input. It provides a localized rate of change, representing the slope of the tangent line to the function at any given point. When this process is applied systematically across the entire domain of the function, it yields a new function—the derivative function—which ...

The derivative measures how the dependent variable changes with respect to the independent variable.

Graphically, the derivative is the limit of the average rate of change as the interval approaches zero.

In mathematical terms, the derivative function, f′(x), assigns a slope to each point on the graph of f(x) —showin...