The derivative is often described as the instantaneous rate of change, the ratio of the instantaneous change in the dependent variable to that of the independent variable. [1] The …

Nov 16, 2022 · In this section we define the derivative, give various notations for the derivative and work a few problems illustrating how to use the definition of the derivative to actually …

Dec 12, 2025 · derivative, in mathematics, the rate of change of a function with respect to a variable. Derivatives are fundamental to the solution of problems in calculus and differential …

Dec 7, 2025 · This page defines the derivative of a function, focusing on tangent and secant lines. It explains that the slope of a secant line is calculated using the difference quotient, while the …

A derivative is the rate of change of a function with respect to a variable. The derivative of a function f (x) is denoted by f' (x) and it can be found by using the limit definition lim h→0 (f …

Just like a slope tells us the direction a line is going, a derivative value tells us the direction a curve is going at a particular spot. At each point on the graph, the derivative value is the slope …

The derivative of a function tells us a lot about the function itself. In a later section, we’ll do in-depth analyses of functions using the first and second derivatives.

The derivative of a function is the rate of change of the function's output relative to its input value. Given y = f (x), the derivative of f (x), denoted f' (x) (or df (x)/dx), is defined by the following …

It means that, for the function x 2, the slope or "rate of change" at any point is 2x. So when x=2 the slope is 2x = 4, as shown here: Or when x=5 the slope is 2x = 10, and so on. Note: f’ (x) …

Nov 10, 2025 · The derivative measures the rate of change of a function at a point, representing the slope of the tangent line to the curve at that point.