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What is e and ln(x)? (Euler's Number and The Natural Logarithm)

Mathacy

925,734 views

Euler's Number, e, is one of the most prominent constants in mathematics and exponential functions are some of the most important in maths. In this video: we take a deep dive into what Euler's Number is, what exponential functions are and how to differentiate them and we take a look at the super important natural logarithm, ln(x).

Website: http://mathacy.com

Timestamps:
0:00 - Intro
0:27 - Compound interest
2:37 - Defining e (Euler's Number)
3:30 - Differentiating exponential functions
6:10 - Derivative of e^x
6:48 - The Natural Logarithm - ln(x)
8:22 - Derivative of ln(x)

20 Comments

@flazzies 10 months ago

wtf did i just watch bro this shit went through my right ear out to my left ear

@sw-reload9232 2 years ago

The explanation feels like getting an eureka moment every 5 seconds or so. Realizing all the connection you've learned in math

@dancl8674 1 year ago

9:33 'we can swap the lim and ln' because, you know, we can just do that... ME: 😵‍💫

@angrwl 5 years ago

Spent hours trying to understand what is eulers constant and got it straightaway by looking at this. Thanks a lot.

@finleycooper8844 3 years ago

Just a heads up 'e' is Euler's number. Euler's Constant is a different constant (Also called the Euler-Mascheroni constant sometimes) and is denoted by a lowercase gamma

@kennethchao1290 2 years ago

anyone still confused here?

@rickintexas1584 3 years ago

I wish I had YouTube when I was in college. I graduated with a BS Aeronautical Engineering in 1986.

@Metal_Icarus 1 year ago

Its crazy how one letter can encompass thousands of human lives of research into mathematics. This video helped me grasp this wonderous number.

@newsgo1876 3 years ago

It is worth emphasizing that "e" is a number defined through the limit operation. And it happens to show an unique property in another limit operation, i.e. the derivative, that e^x has itself as its derivative. This is one of the wonders associated with the limit operation and the infinity process. Essentially, a number is just a symbolic name for a bunch of operations, except the symbols for the natural number 0~9.

@mlarson154 1 month ago

Fascinating... and now my brain hurts.

@Darkmatter321 1 year ago

I'e never enjoyed a video I didn't understand as much as this one

@AimerBoy-t2z 2 years ago

I WAS VERY HELPLESS ON YOUTUBE TO FIND OUT A RIGHT VIDEO TO LEARN THESE LESSONS. THEN THIS ONE CAME. THANKS A LOT. LOVE FROM INDIA

@yassinenajar4369 3 years ago

This has the same feeling as discovering lost lore that's filled with plot twists

@karimjanmohamed3835 5 years ago

Doesn’t get better than this when it comes to explanation. Thanks!

@emmanuelonah4596 2 years ago

Wow! You virtually connected various aspects of mathematics in a very interesting way! Thank you!

@arjun_12 3 years ago

U thought us calculus in the simplest way possible than any schools or coaching institutes did.

@jamesbentonticer4706 4 years ago

This is great. I never understood where the decay function y=e^-×ln (2) actually came from! Fantastic thanks.

@henrynwosu6277 3 years ago

Omo. I hope I get to meet this man someday and thank him personally. Because you're out there giving meaning to my engineering degree and helping me see these things intuitively. Allowing me to chase my passion for Mathematics. Thank you isn't enough. Hopefully I can do something for you too.
Thanks @Mathacy

@bluestar2253 3 months ago

This is by far the best explanation of "e" I have ever watched! Thank you!

@shyyongc.9477 3 years ago

Very well explained video! Made the "e" great again, and really this should be taught in colleges/unis to get students understand the intuition behind