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 …

It is all about slope! Slope = Change in Y / Change in X. We can find an average slope between two points. But how do we find the slope at a point?

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 …

6 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 …

The derivative of a function is itself a function, so we can find the derivative of a derivative. For example, the derivative of a position function is the rate of change of position, or velocity.

Dec 7, 2025 · 2.1 The Definition of the Derivative Learning Objectives Given a curve and a specific point, calculate the slope of the tangent line using the limit of the difference quotient, …

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 …

Derivative definition The derivative of a function is the ratio of the difference of function value f (x) at points x+Δx and x with Δx, when Δx is infinitesimally small.

Explore the fundamentals of derivatives, including types, basic rules, 2nd derivative, implicit differentiation, and derivatives of trigonometric and inverse functions.

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.