LATIN DICTIONARYLexicon Latīnum
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“derive” in Latin

The English word derive itself goes back to Latin dē, through dērīvō.

Riddle & Arnold A Copious and Critical English–Latin Lexicon, 1864

derive
To derive his genealogy or origin from anybody, genus deducere ab aliquo; originem ducere, or trahere, ab aliquo; oriundum esse ab aliquo (to descend from anybody, of more remote descent); originem sui ad aliquem referre (to trace one’s origin to anybody, by a very remote descent): to derive anything from the Deity, Deum facere alicujus rei effectorem.
To derive words from roots or other words; to derive one word from another, esse puto, ducere, or deducere a or ex, etc.; verbum ducere or flectere a, etc.: verbum derivare, or denominare a, etc. (to form one word from another existing word, as “Pelides” from “Peleus;” ☞ but not in the sense of, supposing one word to be the root of another = verbum ducere, etc.): to derive a word from the Greek, flectere verbum de Graeco (Gell., 4, 3): to derive the name of anything from a certain word, nomen alicujus rei a verbo quodam ducere: from what do you think the name of Neptune is derived? unde nomen Neptuni dictum, or ductum, esse putas? Janus is derived from ire; nomen Jani ab eundo ductum est (Cic.).”Facio” is derived from “facies,” proprio nomine dicitur facere a facie (Varr.). I suppose “amicitia” to be derived from “amare,” *amicitiam ab amando ductam, appellatam, fictam, dictam (☞ not derivatam), puto.
Draw from a source or channel, derivare (PROP. and figuratively); from a source, ex fonte [Quint.], fonte [Hor.]; to ... in with accusative: to derive the various secondary meanings of a word from its primary signification, *multiplices vocis significationes a nativa ducere.

Quick answer

What is the Latin word for derive?
The usual Latin words for “derive” are trahō, dērīvō, dūcō. The right choice depends on the sense; see the distinctions below.

Entry from J. E. Riddle & T. K. Arnold, A Copious and Critical English–Latin Lexicon (rev. C. Anthon, New York: Harper, 1864), digitised by Fergus J. P. Walsh, CC BY-SA 4.0; Latin markup adapted by latindictionary.co.