# ∂

It has been suggested that this article be merged with Partial_derivative#Notation. (Discuss) Proposed since December 2018. |

The character **∂** (Unicode: U+2202) is a stylized cursive *d* mainly used as a mathematical symbol to denote a partial derivative such as (read as "the partial derivative of *z* with respect to *x*").^{[1]}

## Contents

## HistoryEdit

The symbol was originally introduced in 1770 by Nicolas de Condorcet, who used it for a partial differential, and adopted for the partial derivative by Adrien-Marie Legendre in 1786.^{[2]}
It represents a specialized cursive type of the letter *d*, just like the integral sign originates as a specialized type of a long s (first used in print by Leibniz in 1686).
Use of the symbol was discontinued by Legendre, but it was taken up again by Carl Gustav Jacob Jacobi in 1841,^{[3]} whose usage became widely adopted.^{[4]}

## Names and codingEdit

The symbol is variously referred to
"curly d", "rounded d", "curved d", or "Jacobi's delta",^{[4]}
or as "del"^{[5]} (but this name is also used for the "nabla" symbol ∇).
It may also be pronounced simply "dee",^{[6]} or "partial dee".^{[7]}^{[8]} "doh",^{[9]} "die"^{[10]} or "dabba".^{[11]}

The Unicode character is accessed by HTML elements `∂`

or `∂`

, the LaTeX symbol (Computer Modern glyph: ** **) is accessed by `\partial`

.

## UsesEdit

**∂** is also used to denote the following:

- The Jacobian .
- The boundary of a set in topology.
- The boundary operator on a chain complex in homological algebra.
- The boundary operator of a differential graded algebra.
- The Dolbeault operator on complex differential forms.

## See alsoEdit

- Differential operator#Notations
- List of mathematical symbols
- 𝒹 (Unicode MATHEMATICAL SCRIPT SMALL D)
- ꝺ (lowercase
*d*in Insular script) *δ*(lowercase Greek Delta)*д*(lowercase Cyrillic De, looks similar when italicized in some typefaces)

## ReferencesEdit

Look up in Wiktionary, the free dictionary.∂ |

**^**Christopher, Essex (2013).*Calculus : a complete course*. p. 682. ISBN 9780321781079. OCLC 872345701.**^**Adrien-Marie Legendre, "Memoire sur la manière de distinguer les maxima des minima dans le Calcul des Variations,"*Histoire de l'Academie Royale des Sciences*(1786), pp. 7–37.**^**Carl Gustav Jacob Jacobi, "De determinantibus Functionalibus,"*Crelle's Journal***22**(1841), pp. 319–352.- ^
^{a}^{b}"The 'curly d' was used in 1770 by Antoine-Nicolas Caritat, Marquis de Condorcet (1743-1794) in 'Memoire sur les Equations aux différence partielles,' which was published in Histoire de L'Academie Royale des Sciences, pp. 151-178, Annee M. DCCLXXIII (1773). On page 152, Condorcet says:*Dans toute la suite de ce Memoire, dz & ∂z désigneront ou deux differences partielles de z, dont une par rapport a x, l'autre par rapport a y, ou bien dz sera une différentielle totale, & ∂z une difference partielle.*

*Pour éviter toute ambiguité, je répresentarie par ∂u/∂x le coefficient de x dans la différence de u, & par du/dx la différence complète de u divisée par dx.*

*Sed quia uncorum accumulatio et legenti et scribenti molestior fieri solet, praetuli characteristica d differentialia vulgaria, differentialia autem partialia characteristica ∂ denotare.*

**^**Bhardwaj, R.S. (2005),*Mathematics for Economics & Business*(2nd ed.), p. 6.4**^**Silverman, Richard A. (1989),*Essential Calculus: With Applications*, p. 216**^**Pemberton, Malcolm; Rau, Nicholas (2011),*Mathematics for Economists: An Introductory Textbook*, p. 271**^**Munem, Mustafa; Foulis, David (1978).*Calculus with Analytic Geometry*. New York, NY: Worth Publishers, Inc. p. 828. ISBN 0-87901-087-8.**^**Bowman, Elizabeth (2014),*Video Lecture for University of Alabama in Huntsville***^**Christopher, Essex; Adams, Robert Alexander (2014).*Calculus : a complete course*(Eighth ed.). p. 682. ISBN 9780321781079. OCLC 872345701.**^**Gokhale, Mujumdar, Kulkarni, Singh, Atal,*Engineering Mathematics I*, p. 10.2, Nirali Prakashan ISBN 8190693549.