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 …

4 days ago · 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 …

Nov 14, 2025 · Calculate the derivative of a given function at a point. Describe the velocity as a rate of change. Explain the difference between average velocity and instantaneous velocity. Estimate the …

A derivative in calculus is the instantaneous rate of change of a function with respect to another variable. Differentiation is the process of finding the derivative of a function.

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 compute the …

A derivative represents the rate at which something changes—think of it as measuring how fast a quantity is changing at any given moment. In this comprehensive guide, we'll explain what …

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 of the tangent …

Comprehensive introduction to derivative definition, one-sided derivatives, differentiability and continuity, and basic differentiation rules.

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 …