17

Differentiating functions of a vector variable

**17.1 Differentiating functions of a vector variable**

In Part Two, we considered continuity and limiting properties of real-valued functions of a real variable – functions defined on a subset of **R.** In Part Three we extended these ideas to functions between metric spaces, or between topological spaces. In particular, these results apply to functions of several real variables – functions defined on a subset of **R**^{d}.

We now turn to differentiation. This involves linearity: we therefore consider functions defined on a subset *U* of a real normed space (*E*, ||.||_{E}) taking values in a real normed space (*F*, ||.||_{F}). In fact, our principal concern will be with functions of several real variables (functions defined ...

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