The Spanish verb 'despedir' (meaning 'to dismiss' or 'to say goodbye') comes from combining two elements: the prefix 'des-' (meaning 'away' or 'apart') and the verb 'pedir' (meaning 'to ask for'). The verb 'pedir' itself comes from Latin 'petere', which meant 'to seek' or 'to request'. When the negative prefix 'des-' was added to 'pedir', the resulting word 'despedir' took on the sense of sending someone away or parting from them, hence its modern meaning of dismissing someone or saying goodbye.

The simpler and more common Spanish verb 'pedir' (meaning 'to ask for' or 'to request') is directly related to 'despedir'. While 'pedir' retained the basic meaning of requesting or asking for something from Latin 'petere', adding the prefix 'des-' transformed the meaning to focus on the act of sending away or parting.

Several English words are related to 'despedir' through the Latin root 'petere', including 'petition' (a formal request), 'compete' (literally 'to seek together'), and 'appetite' (a seeking after food). While these English words maintained connections to the original meaning of seeking or requesting, the Spanish 'despedir' developed in a different direction to express the concept of dismissal or farewell.