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1570s, from Latin exudare/exsudare "ooze out like sweat," from ex- "out" (see ex-) + sudare "to sweat" (see sweat). Related: Exuded; exudes; exuding.
exude ex·ude (ĭg-zōōd', ĭk-sōōd')v. ex·ud·ed, ex·ud·ing, ex·udes To ooze or pass gradually out of a body structure or tissue.