1530s, "irritate, provoke to anger," from Latin exasperatus, past participle of exasperare "make rough, roughen, irritate, provoke," from ex "out, out of; thoroughly" (see ex-) + asper "rough" (see asperity). Related: Exasperated; exasperating.
word-forming element, in English meaning usually "out of, from," but also "upwards, completely, deprive of, without," and "former;" from Latin ex "out of, from within; from which time, since; according to; in regard to," from PIE *eghs "out" (source also of Gaulish ex-, Old Irish ess-, Old Church Slavonic izu, Russian iz). In some cases also from Greek cognate ex, ek. PIE *eghs had comparative form *eks-tero and superlative *eks-t(e)r-emo-. Often reduced to e- before -b-, -d-, -g-, consonantal -i-, -l-, -m-, -n-, -v- (as in elude, emerge, evaporate, etc.).
c. 1200, asprete "hardship," from Old French asperité "difficulty, painful situation, harsh treatment" (12c., Modern French âpreté), a figurative use, from Latin asperitatem (nominative asperitas) "roughness," from asper "rough, harsh," which is of unknown origin. The Latin adjective was used also of sour wine, bad weather, and hard times. Figurative meaning "harshness of feeling" in English is attested from 1660s; literal sense of "roughness of surface" is from early 15c.