n. the function δ f(x; ), derived from a given function f between normed spaces and defined on an open domain, for which If this limit, δ f(x; . ), is continuous and linear in h then the function is said to be Fréchet differentiable at x, and the associated linear operator δ f(x; ) is the Fréchet derivative of f at x, often written ∇ f(x). Such a derivative is necessarily a linear Gateaux derivative. For example, if f is a real-valued function on Euclidean space and f has continuous partial derivatives, then the Fréchet derivative may be identified with the gradient. (Named after the French analyst, topologist and probability theorist, Maurice René Fréchet (1878-1973), who pioneered the study of abstract spaces.)