Derby is a city in Lucas County, Iowa, United States. The population was 131 at the 2000 census.
A city with 131 inhabitants! That made me laugh. Even St David's, the UK's smallest city, has a population of 1,800 (ish).
But then I dug around on Wikipedia a little more and discovered this: "In Oregon, Kansas, Kentucky, North Dakota, Minnesota, and Iowa, all incorporated municipalities are cities."
So that explains it.