What's so special about Euler's number e? | Chapter 5, Essence of calculus

What is e? And why are exponentials proportional to their own derivatives? Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/lessons/eulers-number#thanks Home page: https://www.3blue1brown.com Timestamps 0:00 - Motivating example 3:57 - Deriving the key proportionality property 7:36 - What is e? 8:48 - Natural logs 11:23 - Writing e^ct is a choice Corrections: 9:40 - I meant to say "*the derivative of* e to the power of some constant..." 12:30 - What's written as "(1 + r)" should really just be r, by any usual convention for how to write an interest rate. Thanks to these viewers for their contributions to translations Hebrew: Omer Tuchfeld Italian: ang Vietnamese: @ngvutuan2811 ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown