What are derived names?
There are (were) three main nomenclature systems used for naming organic compounds:


Common Name (or trivial name). Under this convention this molecule is neopentane. For alkanes, this naming system is based on the positioning of methyl substituents, and gives rise to the iso-, sec-, neo- namiong prefixes.
Derived Name. Who uses this method these days???? This system identifies the central carbon atom which has the most carbon groups attached, and then names the groups as a prefix, and ends the name with 'methane'. The formula are often written with the central carbon unit in square brackets. You may still see derived names on MSDS/SDS under the 'Other Names' section. Under this system this molecule is tetramethylmethane. I can think of more important things to teach you in class if this is what you are learning. 
IUPAC Name
This is the accepted naming convention in use today, which allows for retained names, which usually have their origins in the trivial naming system. Its naming system is based on a systematic framework and is used universally. In older texts (pre 1970s), it was known as the Geneva system or congress. Under this convention, this molecule is 2,2-dimethylpropane.


I can't even find any decent references for you at this point, but will update if I find some.