
Differentiable Functions on Normed Linear SpacesDOI: 10.2478/v1003701200051 Abstract: In this article, we formalize differentiability of functions on normed linear spaces. Partial derivative, mean value theorem for vectorvalued functions, continuous differentiability, etc. are formalized. As it is well known, there is no exact analog of the mean value theorem for vectorvalued functions. However a certain type of generalization of the mean value theorem for vectorvalued functions is obtained as follows: If  '(x + t · h) is bounded for t between 0 and 1 by some constant M, then  (x + t · h)  (x) ≤ M · h. This theorem is called the mean value theorem for vectorvalued functions. By this theorem, the relation between the (total) derivative and the partial derivatives of a function is derived [23].
