Abstract
We describe an alternative approach to teaching differentiation in normed spaces (or just in R). The emphasis is put on separation of the background material into ‘metric’ and ‘affine’ properties so that the geometric aspects of differentiation can be made more visible. The notion of tangent mappings in metric spaces is described and a composition rule (or a chain rule) for such mappings is shown. Then, basic properties of affine mappings are discussed. These notions and results are combined to provide a conceptually simple definition of differentiation in normed spaces which is equally natural in any dimension.
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