Efficaciously is from efficacious (from Latin efficāx, from efficere 'to accomplish') + -ly. The ancestry passes through Latin efficāx, Latin efficere, and Latin facere. The suffix -ly forms an adverb or adjective from the base, so the English form is shaped by recognizable word formation as well as by its inherited or borrowed base. In present use as an adverb, it means "in a way that produces the intended result effectively", keeping the historical formation close to the word's ordinary semantic work. Related words include efficacious, efficacy, and effect.