# Differentiable Function

Submitted by Isoscel on Thu, 11/22/2007 - 14:49.

Let us consider and two normed vector spaces , an open set in a function and . We shall say that f is differentiable in a if and only if there is linear continuous operator such as

If such a linear continuous operator exists , it is unique and we call the differential of f in a.

If f is differentiable in any we say f is differentiable on and so there is a function

called the first differential of f.