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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it feels like life
Between heaven and earth, e alone is the honored one.
Do not go home until you finish reading the value of E
Trying to figure out e^(iπ) right now
11:22
It feels a number that god made
F E R T I L E B A N D O F P I C R E A T U R E S
People watch TikTok and other short videos for happiness but feel anxious after that, but only those “short videos ” about knowledgeable makes you happy forever
It's really fun to learn about all of this. Until you figure out it's literally all just numbers describing a circle. thats it. a circle is slightly interesting mathematically, and now we have a bunch of constants, describing different points of a circle. sorry for this comment in advance, was just let down by a research angle 🙁
Dude you're smart but you are shit at explaining things.
And for fixed t, e^t is the limit as n goes to infinity of (1+t/n)^n. But surprisingly, e¹ (and similarly, e^(1/t) or e^(2/t) – exceptions at t=1) has a very simple continued fraction: [2; 1, 2, 1, 1, 4, 1, 1, 6, 1, … , 1, 2n, 1…].
Holy e
I already know this
0.253530 90degrees reduction 4 degrees
Those pi creatures are a MACHINE…
Are you for real.. how come no one explains e this way.. I am stuck on this video for last 2 hours .. trying to digest what I learned.
I am watching this in grade e^(2.19722457734)
I am more of a Pi person
this is another masterpiece , daym you should be on imdb
i came here not because i was stuck at math but because i was coding my game engine. its weird how math is just memorise so and so formulas and it feels effortless most of the time as long as you know your formulas well but we never think about the real world consequences of such and such constant or formula. i was coding a frame rate independent exponential decay function and couldnt really grasp it and thats why i came here. had i never got out of my math textbook i would have never thought about why d/dx of e^x is e^x or what e even is really. ill be more cautious about this from now. we miss out on so many things in our textbooks because they weren't presented well but have very real and practical applications!
Que FEO que le llamen dizque ENTRADA, y a la imagen o resultado, dizque SALIDA.
Where to baby pi come from?
Wauuu, al fin fude entender lo que me faltaba de integrales!!! 😮
8:07 well I was just about able to understand what’s going on up to this point. Unfortunately I haven’t touched math in over 10 years so I’m gonna have to go relearn some basic algebra to be able to understand the rest of this, but it is intriguing.
Como sabes cuál constante representa a la función específica que estás usando, en la forma de e elevado a contrast te por t ?
Fantastic explanation, thank you!
Thank you kindly
I'm currently studying engineering maths and I'm curious about this stuff… I don't understand calculus yet, but your presentation is fantastic and this was a very interesting watch!