When something is derived from something else, it is made from that. Ham is derived from pork, and the active ingredient in aspirin is derived from the bark of the willow tree.
It's best to use derived when you can still see the parts of the original in something. Some people believe baseball was derived from the game of cricket. Both games involve batting and runners, but cricket was around first. Derived is also the past tense of the verb, derive, which can mean to figure out or get. After six tries, Lucia derived the answer to the difficult math problem.