derived function vs first derivative

derived function and first derivative both are nouns.

Word	Noun	Adjective	Verb	Adverb
derived function	Yes	No	No	No
first derivative	Yes	No	No	No

As nouns, derived function and first derivative are synonyms defined as:

derived function and first derivative: the result of mathematical differentiation; the instantaneous change of one quantity relative to another; df(x)/dx

Other synonyms of derived function include derivative, differential, differential coefficient.

derived function (noun)	first derivative (noun)
the result of mathematical differentiation; the instantaneous change of one quantity relative to another; df(x)/dx	the result of mathematical differentiation; the instantaneous change of one quantity relative to another; df(x)/dx