"Desultory" means lacking a plan, purpose, or enthusiasm. It describes actions or efforts that are aimless and inconsistent. This fits perfectly with the phrase "lacking purpose or enthusiasm."
Let's look at why the other options are incorrect:
* "Derogatory" means disrespectful or critical. * "Denigrant" is not a recognized word in the English language and likely misspelled. * "Depressive" relates to depression, a mental state characterized by sadness and lack of interest. * "Devious" means deliberately dishonest or straying from the right course.