Final answer:
While Haydn had numerous responsibilities, including composing for family concerts, military bands, private performances, and church services, giving music lessons was not a documented part of his duties while he worked for Prince Esterhazy.
Step-by-step explanation:
When Haydn worked for Prince Esterhazy, he had a wide array of responsibilities. His duties mainly involved composing music for various occasions and ensembles that were part of court life. These included composing music for family concerts, the Prince's military band, and private performances. Additionally, he was also responsible for composing music for church services. Considering the options provided, one duty that Joseph Haydn was not specifically known for doing while in the employ of Prince Esterhazy was: They gave music lessons.