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mathsisfun.com
https://www.mathsisfun.com/calculus/derivatives-in…
Introduction to Derivatives - Math is Fun
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 (x) = x2: Expand (x+Δx) 2 to x 2 +2x Δx+ (Δx) 2: Simplify (x 2 and −x 2 cancel): Simplify more (divide through by Δx):
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wikipedia.org
https://en.wikipedia.org/wiki/Derivative
Derivative - Wikipedia
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 derivative is called differentiation. There are multiple different notations for differentiation.
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britannica.com
https://www.britannica.com/science/derivative-math…
Derivative | Definition & Facts | Britannica
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 or, more precisely, as the slope of the tangent line at a point.
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derivativecalculus.com
https://www.derivativecalculus.com/what-is-derivat…
What is a Derivative? Complete Beginner's Guide
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 derivatives are, why they matter, and how to calculate them.
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lamar.edu
https://tutorial.math.lamar.edu/classes/calcI/Defn…
Calculus I - 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 derivative to actually compute the derivative of a function.
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cuemath.com
https://www.cuemath.com/calculus/derivatives/
Derivatives - Calculus, Meaning, Interpretation - Cuemath
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.
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libretexts.org
https://math.libretexts.org/Bookshelves/Calculus/C…
3.1: Defining the Derivative - Mathematics LibreTexts
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 derivative from a table of values.
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mathwarehouse.com
https://www.mathwarehouse.com/calculus/derivatives…
What is a Derivative? Visual Explanation with color coded examples and ...
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 line at that point.
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mathisimple.com
https://www.mathisimple.com/calculus/course-05-der…
Derivative Definition and Basic Rules | Calculus Course | MathIsimple
Comprehensive introduction to derivative definition, one-sided derivatives, differentiability and continuity, and basic differentiation rules.
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math.net
https://www.math.net/derivative
Derivative - Math.net
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 definition of the derivative is derived from the formula for the slope of a line.