Assuming you have only a tiny piece of paper and want to jot down the gist of the most common uses (each has alternate meanings and many times they can be used interchangeably, either because the speaker is speaking loosely, or figuratively):
1) To understand something : to comprehend it
Do you understand how RNA transcription works?
2) To find something out : to learn about something by asking deliberately
I'll find out when the shop opens tomorrow morning by phoning the proprietor.
b) or accidentally e.g. by overhearing it being spoken about, etc
I found out that Mary and John are going to have a baby. She was trying on maternity clothes in the department store.
3) To discover something : to learn something through experimentation
Vaccines are discovered by scientists.
4) To realize something : to suddenly understand or recall something
I just realized that we cannot go to the beach next Saturday; that's the day of John's wedding.
I just realized that Superman is actually Clark Kent. (or that Clark Kent is actually Superman).
5) To perceive something : to sense something; to "see" it figuratively
I perceived that something was amiss with their relationship. John seemed on edge and Mary was distant.
Yes, this is pretty common usage of got in a casual, conversational context. It's not incorrect, but it is informal. In writing, this usage is generally only appropriate if the author is deliberately evoking an informal, conversational tone.
In general, one would instead use found, saw, or another more traditional verb.
Best Answer
According to the Cambridge Dictionary, the verb derive means "to get something from something else". You use it in a sentence like this:
Compare that with your sentence:
Note that there is no verb object in your sentence. You can correct it by adding a verb object like this:
You would be more likely to convert this to a passive voice sentence: