Other forms: duteously
To be duteous is to be conscious of your duties and diligent in performing them. A duteous employee gets to work on time, meets every deadline, and never gossips about the boss.
A duty is a responsibility or obligation, so to be duteous is to be mindful of one’s duties. A doctor who makes a home visit is duteous. A waiter who is quick and accurate is duteous. Being duteous suggests diligence and respect for the task at hand. In some professions — like being a butler — the whole job is based on being duteous, but you can be duteous in any task you take seriously.