Derivative of Exponential Function (e^x) From First Principles

In this video I showed that d/dx (e^x) = e^x using the definition of the derivative.

[AlongCameAirxD]

This is the only video I found that solved this problem and that limit without using the circular logic of L'Hopital's rule. You are the only one that showed that limit to truly be 1. Earned a like from me.

[herbertsusmann]

It has literally been 50 years now since I learned this stuff so many of the details I've forgotten (like how to derive things like this from first principles). This is an elegant way to do that for e^x!

[emmanuelmasemola]

Very sincere, very clear, I wish we were together during my university days, these are the kind of channels that deserve subscription, you don't need to tell us to subscribe, we have fallen inlove with your content.

[nadineabusaleh]

The way he looks at maths as it is magic and charm gave we a really beautiful vibes, i have never seen a teacher that is calm and has this clarity before . I hope he continues .

[AcryllixGD]

Honestly one of the best videos ive ever watched! Im an a level student in the uk learning about calculus and this video made it so clear as to why this was the case! Really good video!

[xebby]

The BEST explanation I've watched about this derivative

[sphakamisozondi]

I have never, not even in my maths books I used at university, have someone explained why, _lim_ _h -->0_ *{exp(h) - 1}/h =1*
Well done sir. Much love from South Africa

[robread-jones]

We all know there is something inherently beautiful in mathematics, but that explanation with its cool, calm, clear and entertaining delivery really emphasized that point. It was a joy to watch.

A video has to be something particularly special to get both a like and a subscribe out of a grumpy old git like me. Job done here. I'm looking forward to watching more of your videos.

[Katutowavicle]

I wanna thank not just for the great explanation but the positive energy you put in the video

[GicaKontraglobalismului]

Great! I have always calculated the derivative of the exponential using the derivative of its inverse, that is, of the logarithm, and always thought the direct calculation impossible.
In Romanian Language "to learn" is said "a invata" which is formed of words "in" and "viata" which mean "in" and "life" ; in other words, the Romanian the word for "to learn" actually means "to be alive" which is exactly what you said in the end. Your mind already thinks Romanian! I also appreciate your style, the blackboard, the chalk, and last but not least your calligraphy!

[MrDipanmehta]

This is the most critical video - unlike so many other dealing with this topic. However, this doesn't comes on top of youtube search try adding some keywords or description mentioning "exponential function". This is amaziing video thank you.

[labibbidabibbadum]

Liked, subscribed, coming back. I’m helping my teenage son who is just starting with calculus. This kind of clarity in teaching is wonderful.

[mihaipuiu]

Sir, you are a good teacher.Why? Because your writing is very nice, you work on a clean table, but very important...your proof is very clear and you explain like MICHAEL PENN. Thanks, SIR.

[debjanimukherjee]

Reminiscing my college days with you and enjoying my retired life ❤

[renesperb]

A nice and clear presentation, and, in contrast to many other videos of this type, a good handwriting, making it easy to read.

[hiderr]

You may want to substitute (e^h - 1) with (1/n) instead of n. This way you would get easily to the most commonly known definition of e, that is lim n->inf (1+1/n)^n instead of (1+n)^(1/n)

[goldCrystalhaze]

I saw an explanation of the derivative of a^x in a lecture, which I never actually understood and I was going to search for a better explanation these days. Your video came by chance and it is fantastic! Thank you so much! I have subscribed to your channel.

[donald_w]

You are an incredible teacher! Thank you for explaining this so well and not overlooking the small details 😊

[MrWildcathendrix]

I've just studied this demonstration in my Math 1 book for my first year of Computer Science Engineering university course, it's exactly the same as you write, but the way that you explain it makes math much more fun!

[obadamh]

I finally found someone to clear it up simply, I really owe you