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Second derivative

In calculus, the second derivative, or the second-order derivative, of a function f is the derivative of the derivative of f. Informally, the second derivative can be phrased as "the rate of change of the rate of change"; for example, the second derivative of the position of an object with respect to time is the instantaneous acceleration of the object…

Generalization to higher dimensions, Relation to the graph & Limit

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Overview

Second derivative power rule

Notation

Relation to the graph

Limit

Quadratic approximation

Eigenvalues and eigenvectors of the second derivative

Generalization to higher dimensions

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Map overview Semantic statistics

Second derivative

Nodes54
Edges53
Triples41
Avg. degree1.96
Density0.037037
Components1

How this topic connects Entity context

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Second derivative

Top relations

related to The Hessian · 6
Second derivative → For, Hessian, If, R3, See, The
related to The Laplacian · 6
Second derivative → Another, Delta, Hessian, Laplacian, The Laplacian, This
related to Notation · 5
Second derivative → Leibniz's, That, The, This, When
related to Eigenvalues and eigenvectors of the second derivative · 4
Second derivative → Dirichlet, Eigenvalues, For, Here
related to Quadratic approximation · 4
Second derivative → Just, Taylor, The, This
related to Second derivative test · 3
Second derivative → If, Specifically, The
related to Concavity · 2
Second derivative → Similarly, The
related to Example · 2
Second derivative → Given, The
related to External links · 2
Second derivative → Discrete Second Derivative, Unevenly Spaced Points
related to Inflection points · 2
Second derivative → Assuming, If

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Important terminology

derivative second displaystyle function calculus frac graph limit point f'' velocity position time eigenvalues test isbn partial negative acceleration quadratic

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Second derivativeis aLaplacian0.90text
Second derivativerelated to ConcavityThe0.60section
Second derivativerelated to ConcavitySimilarly0.60section
Second derivativerelated to Eigenvalues and eigenvectors of the second derivativeFor0.60section
Second derivativerelated to Eigenvalues and eigenvectors of the second derivativeDirichlet0.60section
Second derivativerelated to Eigenvalues and eigenvectors of the second derivativeHere0.60section
Second derivativerelated to Eigenvalues and eigenvectors of the second derivativeEigenvalues0.60section
Second derivativerelated to ExampleGiven0.60section
Second derivativerelated to ExampleThe0.60section
Second derivativerelated to External linksDiscrete Second Derivative0.60section
Second derivativerelated to External linksUnevenly Spaced Points0.60section
Second derivativerelated to Inflection pointsIf0.60section

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    Min side: 3
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