I looked up the term pissant {piss-ant}, at the following dictionary website, http://info.babylon.com/onlinebox.cgi?rt=ol&cid=CD776&term=pissant&tl=English&uil=English&tid=AffToolbar. This is the definition from that website, "A pissant, also seen as piss-ant and piss ant, is one or the other of two specific types of ant. The word can also refer to an inconsequential, irrelevant, or worthless person, especially one who is irritating or contemptible out of proportion to his significance. Its origin is with pismire, a 14th-century word for ant."

You have asked two separted questions in this hub so, to answer the first question, what is a pissant? A pissant is a type of ant. To answer your second question, is it a derogatory term? Yes, I believe it is. As you can see in the above definition, it states that a pissant can refer to an inconsquential, irrelevant or worthless person. I would think that if you were going to call someone worthless that would be considered derogatory. To be a derogatory term, it would mean that you were belittling that person. Calling a person worthless is definitely belittling that person.

Soruces: Babylon English Dictionary Website,  http://info.babylon.com/onlinebox.cgi?rt=ol&cid=CD776&term=pissant&tl=English&uil=English&tid=AffToolbar