Demystifying the Exponential Function: The Complete Beginner's Guide
In this video, I explain what the exponential function is, why the definition of the exponential function involves its own derivative, the types of phenomena that the exponential function can model. We will also learn how to perform calculations with the exponential function and explore the formula of the exponential function in the form of an infinite sum.
00:00 Introduction
00:26 Motivation: What We Aim to Model
02:22 Recall: Connection Between Derivative and Tangent
03:45 Defining the Exponential Function
06:24 The Fundamental Property of Exponential Functions
07:44 The Underlying Formula
14:15 Performing Calculations with Exponentials