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In these posts I will not be explaining all of the basic mathematical concepts which are required to appreciate the main discussion, so they are not aimed at the novice, as it were. I would guess maybe that a second-year university student in mathematics will be able to fully appreciate these posts.
Recently, I have been thinking about differentiation and in this post I would like to discuss some ways of approaching the concept, starting right from the basics. In this first post, we’ll discuss some approaches to the idea of differentiation. I want to settle on a certain geometric perspective and then generalise it to higher dimensions. The aim is to shed light on why the definition of the derivative of a function generalises as it does.