## Differential calculus |

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In **differential calculus** is a subfield of ^{[1]} concerned with the study of the rates at which quantities change. It is one of the two traditional divisions of calculus, the other being ^{[2]}

The primary objects of study in differential calculus are the **differentiation**. Geometrically, the derivative at a point is the

Differential calculus and integral calculus are connected by the

Differentiation has applications to nearly all quantitative disciplines. For example, in **F** = *m***a** equation associated with

Derivatives are frequently used to find the

Suppose that *x* and *y* are *y* is a *x*, that is, for every value of *x*, there is a corresponding value of *y*. This relationship can be written as *y* = *f*(*x*). If *f*(*x*) is the equation for a straight line (called a *m* and *b* such that *y* = *mx* + *b*. In this "slope-intercept form", the term *m* is called the

where the symbol Δ (the uppercase form of the *y* = *m* Δ*x*.

A general function is not a line, so it does not have a slope. Geometrically, the **derivative of f at the point x = a** is the slope of the

If every point *a* in the domain of *f* has a derivative, there is a function that sends every point *a* to the derivative of *f* at *a*. For example, if *f*(*x*) = *x*^{2}, then the derivative function *f* ′(*x*) = *dy*/*dx* = 2*x*.

A closely related notion is the *x* and *y* are real variables, the derivative of *f* at *x* is the slope of the tangent line to the graph of *f* at *x*. Because the source and target of *f* are one-dimensional, the derivative of *f* is a real number. If *x* and *y* are vectors, then the best linear approximation to the graph of *f* depends on how *f* changes in several directions at once. Taking the best linear approximation in a single direction determines a *y*/∂*x*. The linearization of *f* in all directions at once is called the

Other Languages

Afrikaans: Differensiaalrekening

Alemannisch: Differentialrechnung

العربية: تفاضل

অসমীয়া: অৱকলন

asturianu: Cálculu diferencial

বাংলা: অন্তরকলন

Bân-lâm-gú: Bî-hun

беларуская: Дыферэнцыяльнае злічэнне

беларуская (тарашкевіца): Дыфэрэнцыйнае зьлічэньне

Boarisch: Differenziäurechnung

català: Càlcul diferencial

Чӑвашла: Дифференциалла шутлани

čeština: Diferenciální počet

Cymraeg: Calcwlws differol

dansk: Differentialregning

Deutsch: Differentialrechnung

eesti: Diferentsiaalarvutus

Ελληνικά: Διαφορικός λογισμός

español: Cálculo diferencial

Esperanto: Diferenciala kalkulo

euskara: Kalkulu diferentzial

فارسی: حساب دیفرانسیل

Gaeilge: Calcalas difreálach

galego: Cálculo diferencial

客家語/Hak-kâ-ngî: Mì-fûn

հայերեն: Դիֆերենցիալ հաշիվ

हिन्दी: अवकल गणित

hrvatski: Diferencijalni račun

Bahasa Indonesia: Kalkulus diferensial

íslenska: Deildun

ქართული: დიფერენციალური აღრიცხვა

Latina: Calculus differentialis

lietuvių: Išvestinė

Limburgs: Differentiaalraekening

magyar: Differenciálszámítás

मराठी: भैदिक कलन

مصرى: اشتقاق

Nederlands: Differentiaalrekening

日本語: 微分法

norsk nynorsk: Differensialrekning

oʻzbekcha/ўзбекча: Differensial hisob

Piemontèis: Càlcol diferensial

polski: Różniczka funkcji

русский: Дифференциальное исчисление

Scots: Differential calculus

sicilianu: Càlculu diffirinziali

සිංහල: අවකලනය

Simple English: Differential calculus

SiSwati: Differential calculus

svenska: Differentialkalkyl

Tagalog: Kalkulus na diperensiyal

தமிழ்: வகை நுண்கணிதம்

Türkçe: Diferansiyel kalkülüs

українська: Диференціальне числення

اردو: تفریقی حسابان

Tiếng Việt: Vi phân

吴语: 微分学

粵語: 微分

中文: 微分学