ABSTRACT
The definition of the derivative of a function g : D ⊆ R→ R is a familiar one. In this chapter we examine various ways in which this definition can be extended to functions f : D ⊆ RJ → R of several variables. Here D is the domain of the function f and we assume that int(D), the interior of the set D, is not empty. While the concepts of directional derivatives and gradients are familiar enough, they are not the whole story of differentiation. In this chapter we consider the Gaˆteaux derivative and the Fre´chet derivative, along with several examples. This chapter can be skipped without harm to the reader.
