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Derivative

In mathematics, the derivative is a fundamental tool that quantifies the sensitivity to change of a function's output with respect to its input. The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point. The tangent line is the best linear…

Generalizations, Definition & Notation

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Overview

Definition

Continuity and differentiability

Notation

Rules of computation

Antidifferentiation

Higher-order derivatives

In other dimensions

Generalizations

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Derivative

Nodes133
Edges132
Triples144
Avg. degree1.99
Density0.015038
Components1

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Derivative

Top relations

related to Generalizations · 17
Derivative → An, Another, Banach, Cauchy, Derivations, Differentiation, Fréchet, Gateaux, Here, If, Intuitively, Nevertheless, One, Properties, Riemann, The, This
related to Continuity and differentiability · 16
Derivative → As, Consequently, Early, Even, For, However, If, In, Informally, Lipschitz, Most, Stefan Banach, The, This, Under, Weierstrass
related to Notation · 16
Derivative → Another, Bigl, Bigr, For, Gottfried Wilhelm Leibniz, Higher, It, Joseph-Louis Lagrange, Leibniz, One, Roman, Similarly, The, These, This, Unlike
related to External links · 12
Derivative → EMS Press, Encyclopedia, Eric, Khan Academy, Leibniz, Mathematics, MathWorld, Newton, Online Derivative Calculator, Usain Bolt, Weisstein, Wolfram Alpha
related to Total derivative and Jacobian matrix · 10
Derivative → Here, However, If, Jac, Jacobian, Similarly, That, The, This, When
related to Higher-order derivatives · 9
Derivative → Any, As, By, For, Given, Higher-order, If, One, The
related to Partial derivatives · 8
Derivative → As, For, Functions, Here, In, It, Partial, To
related to Rules for combined functions · 8
Derivative → As, Chain, Constant, If, Product, Quotient, Sum, The
related to Using infinitesimals · 8
Derivative → In, Leibniz, One, Such, Taking, The, This, Thus
related to As a limit · 7
Derivative → If, It, Multiple, Notation, See, The, This

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Important terminology

displaystyle function derivatives functions partial differentiable frac f' example vector point notation called mathbf respect continuous variables tangent differentiation real

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Derivativeis afundamental tool that quantifies the sensitivity to change of a function's output with respect to its input0.90text
Derivativeis aslope of the line through two points on the graph of the function0.90text
Derivativeis aslope of the tangent.Using infinitesimalsOne way to think of the derivative d f d x0.90text
Derivativeis aslope of the tangent0.90text
Derivativeis aderivative of the0.90text
the derivativeinstance ofThis provides a way to define the basic concepts of calculus0.80text
integral in terms of infinitesimalsinstance ofThis provides a way to define the basic concepts of calculus0.80text
thereby giving a precise meaning to the dinstance ofThis provides a way to define the basic concepts of calculus0.80text
Derivativerelated to AntidifferentiationAn0.60section
Derivativerelated to AntidifferentiationAntiderivatives0.60section
Derivativerelated to AntidifferentiationThe0.60section
Derivativerelated to AntidifferentiationMore0.60section

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