View source for Derivation

{{also|Derivation|dérivation}}
==English==

===Etymology===
From {{inh|en|enm|derivacioun}}, borrowed from {{der|en|frm|dérivation}}, from {{der|en|la|derivatio|dērīvātiō, dērīvātiōnem}}.
Morphologically {{suffix|en|derive|ation|nocat=1}}

===Pronunciation===
* {{IPA|en|/ˌdɛ.ɹɪˈveɪ.ʃ(ə)n/}}
* {{audio|en|en-uk-derivation.ogg|a=UK}}
* {{rhymes|en|eɪʃən|s=4}}

===Noun===
{{en-noun|~}}

# A [[leading]] or [[drawing]] off of [[water]] from a [[stream]] or [[source]].
# The act of [[receiving]] anything from a [[source]]; the act of [[procuring]] an effect from a [[cause]], [[means]], or [[condition]], as [[profits]] from [[capital]], [[conclusions]] or [[opinions]] from [[evidence]].
# {{lb|en|genealogy|linguistics}} The act of [[tracing]] [[origin]] or [[descent]]; an instance thereof (for example, an [[etymology#English:_an account of the origin and development of a word|etymology]]).
#: {{usex|en|the '''derivation''' of a word from an [[Indo-European]] root}}
# {{lb|en|grammar}} Forming a new word by changing the base of another word or by adding affixes to it.
# The state or [[method]] of being [[derived]]; the [[relation]] of [[origin]] when [[established]] or [[asserted]].
# That from which a thing is [[derived]].
# That which is [[derived]]; a [[derivative]]; the result of a [[deduction]].
# The process of [[derive|deriving]] one thing from another, especially in [[logic]]; a [[deduction]].
## {{lb|en|mathematics}} A [[formal]] [[proof]]: a [[sequence]] of statements, each of which is logically [[entail]]ed  by those preceding (with respect to some  collection of [[rule of inference|rules of inference]]), the initial statements being taken as [[axiom]]s.
# {{lb|en|mathematics|calculus}} The process of [[application]] of the [[derivative]] [[operator]] to a [[function]], yielding another function called the [[derived function]] of the first.
# {{lb|en|mathematics|{{w|differential algebra}}}} An [[algebraic]] [[generalization]] of the [[derivative]] operator (from its natural setting in the [[ring]] of real-valued functions) to a general [[associative algebra]] over a [[field]]. Formally, (''given an algebra <math>A</math> over a field <math>K</math>'') a <math>K</math>-linear [[endomorphism]] that satisfies {{w|Product_rule#Derivations_in_abstract_algebra_and_differential_geometry|Leibnitz's Law}}.
## ''Any of several generalizations of this notion: a {{w|Hasse–Schmidt derivation}}, a {{w|Derivation_(differential_algebra)#Graded_derivations|graded derivation}}, etc.''
# {{lb|en|medicine|historical}} A [[drawing]] of [[humors]] or [[fluids]] from one part of the [[body]] to [[another]], to [[relieve]] or [[lessen]] a [[morbid]] [[process]].

====Derived terms====
{{col|en|biderivation|derivationism|derivationist|misderivation|quasiderivation|rederivation|subderivation|superderivation
|derivational|derivation tree|zero derivation}}

====Related terms====
* {{l|en|derive}}
* {{l|en|derived}}
* {{l|en|derivative}}

====Translations====
{{trans-top|leading or drawing off of water}}
* Bulgarian: {{t|bg|деривация}}
* Finnish: {{t+|fi|juoksutus}}
* Italian: {{t+|it|deviazione|f}}
* Romanian: {{t+|ro|derivație|f}}
* Swedish: {{t+|sv|avledning|c}}
{{trans-bottom}}

{{trans-top|act of receiving anything from a source}}
* Bulgarian: {{t|bg|извеждане}}
* Czech: {{t|cs|odvození|n}}
* Finnish: {{t+|fi|johtaminen}}
* Hungarian: {{t+|hu|kinyerés}}, {{t+|hu|származtatás}}
* Italian: {{t+|it|derivazione|f}}
{{trans-bottom}}

{{trans-top|act of tracing origin or descent}}
* Bulgarian: {{t+|bg|етимология}}
* Catalan: {{t+|ca|derivació|f}}
* Chinese:
*: Mandarin: {{t+|cmn|派生}}
* Danish: {{t|da|afledning|c}}
* Esperanto: {{t|eo|derivado}}
* Finnish: {{t+|fi|johtaminen}} {{qualifier|grammar}}
* German: {{t|de|Herleiten|n}}, {{t+|de|Herleitung|f}}, {{t+|de|Ableitung|f}}
* Hungarian: {{t+|hu|származtatás}}
* Italian: {{t+|it|etimologia|f}}
* Japanese: {{t+|ja|派生|tr=hasei}}
* Maori: {{t|mi|takenga}}
* Mongolian: {{t+|mn|гарал үүсэл|sc=Cyrl}}
* Norwegian:
*: Bokmål: {{t|nb|avledning|m|f}}, {{t|nb|avleiing|m|f}}
*: Nynorsk: {{t|nn|avleiing|f}}
* Russian: {{t+|ru|происхожде́ние|n}}
* Spanish: {{t+|es|derivación|f}}
* Swedish: {{t+|sv|avledning|c}}, {{t+|sv|härledning|c}}
* Venetan: {{t+|vec|derivasion|f}}
{{trans-bottom}}

{{trans-top|forming a new word by changing the base of another word or by adding affixes to it}}
* Albanian: {{t+|sq|ndajshtesim|m}}
* Azerbaijani: {{t|az|törəmə}}, {{t|az|derivativ}}
* Danish: {{t|da|afledning|c}}, {{t|da|derivation|c}}
* Dutch: {{t+|nl|afleiding|f}}, {{t+|nl|derivatie|f}}
* Georgian: {{t|ka|წარმოქმნა}}, {{t|ka|სიტყვაწარმოქმნა}}, {{t|ka|წარმოება}}, {{t|ka|სიტყვაწარმოება}}, {{t|ka|დერივაცია}}
* Hungarian: {{t|hu|deriváció}}, {{t+|hu|képzés}}, {{t+|hu|szóképzés}}
* Norwegian:
*: Bokmål: {{t|nb|avledning|m|f}}, {{t|nb|avleiing|m|f}}, {{t+|nb|derivasjon|m}}
*: Nynorsk: {{t|nn|avleiing|f}}, {{t|nn|derivasjon|m}}
* Polish: {{t+|pl|derywacja|f}}
* Swedish: {{t+|sv|avledning|c}}
{{trans-bottom}}

{{trans-top|state or method of being derived}}
* Finnish: {{t+|fi|johtaminen}} {{qualifier|state}}; {{t|fi|johto-oppi}} {{qualifier|method}}
{{trans-bottom}}

{{trans-top|that from which sthg is derived}}
* Danish: {{t|da|afledning|c}}
* Finnish: {{t+|fi|kanta}} {{qualifier|linguistics}}
* Hungarian: {{t+|hu|eredet}}, {{t+|hu|kiindulás}}
{{trans-bottom}}

{{trans-top|that which is derived}}
* Danish: {{t|da|afledning|c}}, {{t|da|derivat|n}}
* Finnish: {{t+|fi|johdos}}
* Hungarian: {{t+|hu|származék}}
* Maori: {{t|mi|takenga}}
* Norwegian:
*: Bokmål: {{t|nb|avledning|m|f}}, {{t|nb|avleiing|m|f}}
*: Nynorsk: {{t|nn|avleiing|f}}
* Polish: {{t+|pl|derywacja|f}}
* Swedish: {{t+|sv|avledning|c}}
{{trans-bottom}}

{{trans-top|math: operation of deducing}}
* Bulgarian: {{t|bg|диференциране}}
* Czech: {{t+|cs|derivace|f}}
* Dutch: {{t+|nl|afleiding|f}}
* Finnish: {{t+|fi|johtaminen}}
* Georgian: {{t|ka|გაწარმოება|sc=Geor}}
* German: {{t+|de|Derivation|f}}
* Hungarian: {{t+|hu|deriválás}}
* Norwegian:
*: Bokmål: {{t+|nb|derivasjon|m}}
*: Nynorsk: {{t|nn|derivasjon|m}}
* Romanian: {{t+|ro|derivare|f}}
* Slovak: {{t|sk|derivácia|f}}
* Spanish: {{t+|es|derivada|f}}, {{t+|es|derivación|f}}
* Swedish: {{t+|sv|derivering|c}}, {{t+|sv|härledning|c}}
{{trans-bottom}}

{{trans-top|medicine: drawing of humors or fluids}}
{{trans-bottom}}

{{checktrans-top}}
* Dutch: {{t+|nl|afleiding|f}}
* Punjabi: {{t|pa|ਵਿਉਤਪੱਤੀ|alt=ਵਿਉਤਪੱਤੀ||f}}
{{trans-bottom}}

====Further reading====
* {{R:Webster 1913}}

===See also===
* {{pedia}}

===Anagrams===
* {{anagrams|en|a=adeiinortv|ordinative}}

==Danish==

===Noun===
{{da-noun|en|er}}

# {{lb|da|grammar}} {{l|en|derivation}}

====Declension====
{{da-decl|en|er}}

===Further reading===
* {{R:DDO}}