Differentiability

Part of speech: noun

Definitions

1. This property indicates that a function can be differentiated at any chosen point or consistently across a range of values, reflecting its smoothness
2. A mathematical function exhibits the quality of being differentiable if it can be derived at specific points or overall intervals, indicating consistent smoothness and continuity of its graph
3. The concept of being differentiable signifies that a function has a derivative at all desired points or along selected ranges, showcasing its smooth nature and transition without abrupt changes

Etymology: Differentiability is a plain, built-up word: it takes the adjective "differentiable" and adds the English suffix "-ity", which turns a quality adjective into the noun for that quality. The adjective itself is a chain of parts. The core is "differentiate", borrowed from the New Latin "differentiātus", which draws on Latin "differre", "to carry apart" (from "dis-", "apart", and "ferre", "to carry"), with the sense of distinguishing one thing from another. Attached to this is the Latin-derived suffix "-able", meaning "capable of being", so "differentiable" describes something that can be distinguished, or in mathematics, something that can be differentiated. The suffix "-ity" arrived through Old French "-ité" from Latin "-itās", and it was attached to English adjectives freely from the late Middle Ages onward, so "differentiability" is a modern coinage built from older parts rather than an ancient word. Its mathematical sense depends on the older verb "differentiate", which entered English in the sense of "to make different", with its calculus use following the development of differential calculus in the 17th century.