To exalt is to raise in rank, to glorify, or to increase the effect or intensity of. In all its definitions, exalt is transitive, meaning it takes a direct object (i.e., you can’t just exalt, period; you have to exalt someone or something). The word’s past participle, exalted, is often used to mean elevated in rank or lofty.
To exult is to rejoice greatly or to be jubilant or triumphant. It is always intransitive, meaning it does not have a direct object (i.e., you can’t exult someone or something; you just exult). The most common derivative of exult is the adjective exultant, which means marked by great joy or jubilation.
Clark doesn’t belittle or condescend to her characters, nor does she exalt them. [OC Register]
Instead of being excited by Dinkins, Frank and Estelle exult that George’s name was mentioned to Giuliani by his douche friend Lloyd Braun. [AV Club]
So exalted is medical technology that it has become our de facto God during times of personal health crisis. [OregonLive.com]
Now a constant stream of music and anti-Gaddafi slogans is played from the courthouse to the exultant crowd in the square outside. [This is London]