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?
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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

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