'applaudably' ultimately originates from Latin, specifically from the verb 'plaudere' (and the compounded form 'applaudere' from ad- + plaudere), where 'plaudere' meant 'to strike, clap' and the prefix 'ad-' meant 'to' or 'toward'.

'applaud' came into English via Old French/Middle French 'applaudir' from Latin 'applaudere'; the adjective 'applaudable' was formed by adding the suffix '-able' to mean 'worthy of applause', and the adverb 'applaudably' was formed by adding '-ly' to the adjective.

Initially the root meant 'to clap or strike (with the hands)'; over time it came to mean 'to express approval by clapping' and then extended to describe actions 'deserving approval'—hence 'applaudably' now means 'in a commendable or praiseworthy way'.