first derivative vs differential coefficient

first derivative and differential coefficient both are nouns.

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

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

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

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

first derivative (noun)	differential coefficient (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