curvature vs first derivative

curvature and first derivative both are nouns.

Word	Noun	Adjective	Verb	Adverb
curvature	Yes	No	No	No
first derivative	Yes	No	No	No

As nouns, first derivative is a hypernym of curvature; that is, first derivative is a word with a broader meaning than curvature:

curvature: the rate of change (at a point) of the angle between a curve and a tangent to the curve
first derivative: the result of mathematical differentiation; the instantaneous change of one quantity relative to another; df(x)/dx

Other hypernyms of curvature include derivative, derived function, differential, differential coefficient.

curvature (noun)	first derivative (noun)
the rate of change (at a point) of the angle between a curve and a tangent to the curve	the result of mathematical differentiation; the instantaneous change of one quantity relative to another; df(x)/dx
the property possessed by the curving of a line or surface
(medicine) a curving or bending; often abnormal