differential coefficient vs first derivative

differential coefficient and first derivative both are nouns.

Word	Noun	Adjective	Verb	Adverb
differential coefficient	Yes	No	No	No
first derivative	Yes	No	No	No

As nouns, differential coefficient and first derivative are synonyms defined as:

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

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

differential coefficient (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