To find the derivative of a function y = f (x) we use the slope formula: And (from the diagram) we see that: Now follow these steps: Like this: Example: the function f (x) = x2. The slope formula is: Use f …

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 process of finding a …

The derivative of a function describes the function's instantaneous rate of change at a certain point. Another common interpretation is that the derivative gives us the slope of the line tangent to the …

A derivative in calculus is the rate of change of a quantity y with respect to another quantity x. It is also termed the differential coefficient of y with respect to x.

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 limit: The …

Apr 4, 2022 · The Definition of the Derivative – 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 …

Dec 12, 2025 · Derivative, in mathematics, the rate of change of a function with respect to a variable. Geometrically, the derivative of a function can be interpreted as the slope of the graph of the function …