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

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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.




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Hebrew: Omer Tuchfeld
Italian: ang
Vietnamese: @ngvutuan2811



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posted by Hemme1v