What is Euler’s number and the exponential function?
In this post, we establish and use the formula \frac{d}{dx}(e^{x}) = e^{x} , as a part of the Prelim Maths Advanced course under the topic Exponential and Logarithmic Functions and sub-part The Exponential Function and Natural Logarithms, specifically focusing on the introduction to exponential functions and Euler’s number. We use technology, sketch and explore the gradient function of exponential functions and determine that there is a unique number e \approx 2.71828182845 , for which \frac{d}{dx}(e^{x}) = e^{x} where e is called Euler’s number.
The following two videos cover what Euler’s number is, and why it is so significant in the topic Exponential and Logarithmic Functions.
Part 1
