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

Thanks, man. 🙏🏽

This is why we need to understand compounding

right at the beginning i want to mention. the discrete derivative of 2^n is 2^n, ie 2^n is the e^x for discrete calculus

Thanks a lot 🙏🙏 from india

I know physicists love to do this, but "dt" is not a variable you can just fling around like x. It is part of the Integral and derivative operator, so doing any mathematical operation on it is nonsense.
I know, i know. It works where it's done. That doesn't make it correct and i can assure you, any mathematician cries internally when some physicist throws dt around like a variable to derive some equation.

whats the name of the piano piece at the beggining of every episode?

Beautifully explained

I will probably show all your videos to my child if I am going to have any. It's always fascinating to know these basic yet unknown concepts, during our introductory class of differentiation. In 11 I think we just memorised the stuff or did some basic derivations to get there like for y=a^t we just put both sides a log so this becomes log(y)= t*log(a) and then differentiating it we will get dy/dt=(a^t)*log(a). But your video helped me with its interpretation graphically and thats what I was always looking something's made sense over time but things like these are never taught to us we are just supposed to make sense out of it on our own at the mere age of 16 lol

(2^dt -1)/dt takes the form of 0/0 as dt -> 0 what are your thoughts on that ??

This videos should be persevered in case an apocalypse

I can’t get 3e^3t out by the chain rule intuition, has anyone got it?

beynim kanamaya başladı

Nice explanation

this channel is a boon to humanity 🤯

Features in radioactive decay too :) :)

Not Understanding exponential is biggest mistake

La mejor clase

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i came here not knowing what log is at all but the video amazingly explains more than what my doubt was.. very helpful

"e^x=y is the only function that is its own derivative! 🤓☝️"

x=0: 🗿

Decimal exponentiation

The fact that this content is free is insane.

That’s a two.

The only regret I have is not finding this channel before

10(base e)

I like how u connect the derivative to rate of change everytime and then u try to solve the problems using that concept and not by just putting the formula and getting the solution. Because in my school no one is interested in telling the real application of these concepts

Thank you it was beautiful 🤍

The difference between what actually exists at any given moment and the mathematical representation of that moment is exactly the amount jobs that can be supported by that discrepancy. This is known as The Categorical Bnllsh!t expressed at You^G3tFnck3d

Well statistics has no problem with working with fractions of a person... Does calculus have some moral compass forbidding making fractions of people?

Confusing, but understandable.


So

d/dx(a^t)= ln(a)*a^t?

This is amazing. I love this.

awesome videos

Why don't they teach this in school

I love 4b² channel, it makes every hard problem simpler an easier to understand

This is now clearer in my head than it has ever been, even though I use this all the time.

We got ee-!

Super confusing explanation.

This wkuld have made high school math so much easier

Proud to say that i actl got the pattern before the video got to even talking about there being a pattern

having first watched this as a 16 year old, having not learned a second of calculus, sitting here having gotten back from a 3rd year university class on methods for differential equations, it feels an awful lot like reminiscing about your old school

After about 40 years of my life I finally understood the real meaning behind e. Something is terribly broken in our [math] education systems at schools and universities.

I just love this channel!

I just found a beautiful connection between this and another definition for e.

I tried to model this in desmos to see when this proportionality constant equals 1, but I wanted to sort of generalize it.
So I modeled the equation (y^x-1)/x=1
I did some manipulation
(y^x)/x-(1/x)=1
(y^x)/x=1+1/x
(y^x)/x=(x+1)/x
y^x=x+1
y=(x+1)^(1/x)
y=(1+x)^1/x
In the limit here, x is supposed to be approaching zero.
And if you do this, you get the other famous definition of e! I was not expecting to get this, so the algebraic manipulation wasn't the most clean, I just thought this was a really cool find.

Never thought about how e is derived in this way. Great video!