1610s, from un- (1) "not" + past participle of dismay (v.).
Entries linking to undismayed
un- 1
prefix of negation, Old English un-, from Proto-Germanic *un- (source also of Old Saxon, Old Frisian, Old High German, German un-, Gothic un-, Dutch on-), from PIE *n- (source of Sanskrit a-, an- "not," Greek a-, an-, Old Irish an-, Latin in-), combining form of PIE root *ne- "not." Often euphemistic (such as untruth for "lie").
The most prolific of English prefixes, freely and widely used in Old English, where it forms more than 1,000 compounds. It underwent a mass extinction in early Middle English, but emerged with renewed vigor 16c. to form compounds with native and imported words. It disputes with Latin-derived cognate in- (1) the right to form the negation of certain words (indigestable/undigestable, etc.), and though both might be deployed in cooperation to indicate shades of meaning (unfamous/infamous), typically they are not.
It also makes words from phrases (such as uncalled-for, c. 1600; undreamed-of, 1630s; uncome-at-able, 1690s; unputdownable, 1947, of a book; un-in-one-breath-utterable, Ben Jonson; etc., but the habit is not restricted to un-; such as put-up-able-with, 1812). As a prefix in telegramese to replace not and save the cost of a word, it is attested by 1936.
dismay v.
c. 1300, dismaien, "become or be alarmed, upset, or frightened; to confound, break down the courage of by danger or difficulty or fear of calamity, fill with despairing apprehension;" perhaps formed in Anglo-French or Middle English from dis-, here probably intensive (see dis-), + amaien, esmaien, from Old French esmaier "to trouble, disturb."
This is from Vulgar Latin *exmagare "divest of power or ability" (source of Italian smagare "to weaken, dismay, discourage"), from ex- (see ex-) + Proto-Germanic *magan "to be able" (source also of Old High German magen "to be powerful or able"), from PIE root *magh- "to be able, have power."
There also was an Old French *desmaier (attested only in past participle dismaye), from de-, intensive prefix, + Old French esmaier, which also might be the source of the Middle English word. Spanish desmayer "to be dispirited" is a loan word from Old French. Related: Dismayed; dismaying.