Unit 4 – Sections 3.1 to 3.3
Module Overview
In this unit, we begin our study of derivatives. We begin by defining them as a type of limit and trying to understand what they say about functions. Then, we try to figure out how to evaluate derivatives without the use of limits.
Learning Outcomes
- We begin by defining the derivative and trying to find what it says about the original function. We then try to understand the derivative as a function itself.
- Section 3.1 ends by examining more closely the behaviour of the derivative, as well as a crucial requirement for its existence.
- In Section 3.2, we find that the derivative for many simple functions can be found using mechanical methods far easier and faster than using the limit definition.
- Section 3.3 introduces two rules that allow us to significantly expand the list of functions whose derivative we can take without using limits directly.
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