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.
@lukewarm7465
2 жыл бұрын
Same here
@agytjax
Жыл бұрын
@@lukewarm7465 He could have avoided the complicated route of proving using natural log (ln). Here is the proof : We have e^x.Lim(h->0){(e^h - 1)/h} --- (1) We know that e=Lim(h->0){(1+h)^(1/h)} Substituting the value of 'e' in (1) above, we get : => e^x.Lim(h->0){([1+h]^(h*1/h) - 1)/h} => e^x.Lim(h->0){([1+h]^(1) - 1)/h} => e^x.Lim(h->0){(1+h-1)/h} => e^x.Lim(h->0){(h)/h} => e^x.Lim(h->0){1} => e^x
@sphakamisozondi
7 ай бұрын
Sane here. This is a satisfying explaination to this problem
@boguslawszostak1784
5 ай бұрын
You don't have this problem if you DEFINE ln(x) as the integral from 1 to x of 1/u du, and the function e^x as its inverse function.
@spudhead169
5 ай бұрын
Unfortunately it's still kind of circular. d/dx e^x = e^x is itself a definition of e, in that e is the only value of n that satisfies d/dx n^x = n^x . You cannot prove a definition, if you could you wouldn't need it to be a definition. Trying to prove it will always result in a circular argument with a derivative because such a proof requires the use of the definition of e in some form, and since all definitions are equivalent, using the definition of e is equivalent to using the derivative definition and thus circular.
@nadineabusaleh9401
8 ай бұрын
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 .
@emmanuelmasemola1014
2 жыл бұрын
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.
@herbertsusmann986
27 күн бұрын
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!
@AcryllixGD
2 жыл бұрын
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!
@PrimeNewtons
2 жыл бұрын
Thank you.
@xebby9
2 жыл бұрын
The BEST explanation I've watched about this derivative
@Einstein.Albert.official
11 ай бұрын
man you have a beautyful handwrigting
@robread-jones3698
Жыл бұрын
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.
@sphakamisozondi
7 ай бұрын
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
@MrDipanmehta
2 жыл бұрын
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.
@PrimeNewtons
2 жыл бұрын
Thank you for the suggestion, I have made some changes.
@hiderr6805
Жыл бұрын
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)
@PrimeNewtons
Жыл бұрын
Thank you. I will investigate that option
@labibbidabibbadum
Жыл бұрын
Liked, subscribed, coming back. I’m helping my teenage son who is just starting with calculus. This kind of clarity in teaching is wonderful.
@PrimeNewtons
Жыл бұрын
Thanks for the feedback
@Katutowavicle
Жыл бұрын
I wanna thank not just for the great explanation but the positive energy you put in the video
@mihaipuiu6231
Жыл бұрын
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.
@GicaKontraglobalismului
Жыл бұрын
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!
@PrimeNewtons
Жыл бұрын
Wow! This is inspirational! Thank you for your comment.
@debjanimukherjee502
10 ай бұрын
Reminiscing my college days with you and enjoying my retired life ❤
@renesperb
Жыл бұрын
A nice and clear presentation,and , in contrast to many other videos of this type , a good handwriting , making it easy to read.
@obadamh7030
2 жыл бұрын
I finally found someone to clear it up simply, I really owe you
@donald_w
4 ай бұрын
You are an incredible teacher! Thank you for explaining this so well and not overlooking the small details 😊
@MrWildcathendrix
10 ай бұрын
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!
@mohamedsaith4532
2 жыл бұрын
Wow!!!!!! How amazing explanation 👏🏻👏🏻👏🏻👏🏻👏🏻
@kopisusu3781
2 жыл бұрын
this really cleared things up for me. thankyou very much!
@goldCrystalhaze
Жыл бұрын
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.
@No-cg9kj
9 ай бұрын
e and ln love to sneak their way into everything lol. If you haven't got to calc 2 yet be prepared to see them a lot haha.
@RobertKashila
Ай бұрын
The guy is a logarithmic genius 👌
@SanePerson1
11 ай бұрын
A nice side result from this extremely nice demonstration is hidden in the penultimate line. I'm so accustomed to taking the derivative of e^x, that I forget what constant I should use when taking the derivative of a^x. But the entire derivation you've given doesn't change for that case, EXCEPT that in the middle panel, one should use the base-a log instead of the natural log (ln). so you get (d/dx)a^x = [1/log(e)]a^x, where the log is the base-a log. In particular, this recovers the conversion factor for base-10 log and natural log: 1/log(e) ≈ 2.303.
@kingbeauregard
Жыл бұрын
Oooh, I like your style! You're really clear, and your enthusiasm is infectious. Subscribed!
@souverain1er
10 ай бұрын
Great explanation. Love it. Never learnt this in calculus
@catnip2906
4 ай бұрын
Dear Sir. Thanks for the clarity. I was blind but now I see.
@Ray1tx
8 ай бұрын
Wonderful explanation!
@aram5642
Жыл бұрын
Greatest blackboard and chalk I have seen of all math videos here. The lighting would benefit from some angle or diffusor though ;)
@PrimeNewtons
Жыл бұрын
Thank you. I am still trying to find the pest lighting conditions for videos. I hope the newer videos are better lit in your opinion.
@averagehooligan620
Жыл бұрын
Mindblown. Been searching for this.
@invisiblelemur
11 ай бұрын
Beautiful. Thank you for getting me as excited about this as you are!!
@tafadzwachigumbu4276
Жыл бұрын
This is a very good presentation. Thank you sir.
@PrimeNewtons
Жыл бұрын
Thanks
@agytjax
Жыл бұрын
From 4:35 onwards, you could have avoided the complicated route of proving using natural log (ln). Here is the proof : We have e^x.Lim(h->0){(e^h - 1)/h} --- (1) We know that e=Lim(h->0){(1+h)^(1/h)} Substituting the value of 'e' in (1) above, we get : => e^x.Lim(h->0){([1+h]^(h*1/h) - 1)/h} => e^x.Lim(h->0){([1+h]^(1) - 1)/h} => e^x.Lim(h->0){(1+h-1)/h} => e^x.Lim(h->0){(h)/h} => e^x.Lim(h->0){1} => e^x Q.E.D
@clemensvorbauer1183
10 ай бұрын
no, you are not allowed to take the limit h->0 twice…
@anonymous-ui7il
Жыл бұрын
I am binging on your videos, it has helped me a lot with calculus.
@PrimeNewtons
Жыл бұрын
I'm glad you find them helpful. Thanks for the feedback.
@kiturundee9077
3 жыл бұрын
Beautiful video. Love the energy 😀
@felipecanogiraldo2499
Ай бұрын
Very greatful of this explenation, great teacher, great video, great smile haha. Keep it on like that. Greetings from colombia !
@hiderr6805
Жыл бұрын
What an amazing video! Thank you so much! So cool, the only source I found using only elementary methods...
@PrimeNewtons
Жыл бұрын
Thank you
@user-dp9yn7zf4l
10 ай бұрын
Amazing video, first time learn the derivative of e^x this well! I have a question, when we taking the reciprocal, do we need to show that the denominator is not zero (at about 7:45)?
@sakangbenjamin
6 ай бұрын
Always on point sir God bless for your impactation
@tomvitale3555
7 ай бұрын
We've been saved from destruction and made the world a better place to live! 😁 Excellent description!
@Rob1066-
Жыл бұрын
Great pure math explanations!
@idolgin776
Жыл бұрын
It was really cool when the exponential definition of e popped out. Never seen such manipulation before!
@kemumawhitney5439
2 жыл бұрын
Your classes are enjoyable
@okeuwechue9238
7 ай бұрын
Great explanation. Thnx. An alternative explanation would also be expressing the natural exponential function as a Taylor series expansion and then differentiating each individual term to show that the resultant expression is the same as the original series
@PrimeNewtons
7 ай бұрын
That would not be from first principle, though.
@okeuwechue9238
7 ай бұрын
True :-)@@PrimeNewtons
@icafe36485
2 жыл бұрын
Hi Master, I enjoy your teaching method💐🌹👏
@PrimeNewtons
2 жыл бұрын
Thank you 😊
@binhql
Жыл бұрын
Great! You've just made by day :D Appreciate it a lot.
@PrimeNewtons
Жыл бұрын
Happy to help
@tcmxiyw
9 ай бұрын
I think your explanations are beautiful, but when you say something like “the limit of the function is the function of the limit”, please justify it by saying “because the function is continuous”. It is interesting to note that the derivative of f(x)=e^x at any point can be found once we know f’(0).
@muwememwanza3815
2 жыл бұрын
Great video just learned something new
@theeligator8728
6 ай бұрын
thank you sooo much i love your positivity! keep going +1 follower gonna recommend to my peers.
@HelloBillyyu
2 ай бұрын
Hi I have just watched the video. Great work! Many thanks. Can I explore another approach here? We could find the Maclaurin series of e^h and it is be 1 + h + h^2 / 2 … then (e^h - 1) / h = 1 + h^3/2 + … then the limit of this is 1 if h goes to 0. This method is generally applicable to many ‘nasty’ limit calculations. Happy to chat. Cheers!
@PrimeNewtons
2 ай бұрын
Yes, that's an option. However, this video was to highlight first principles.
@nemo5619
Жыл бұрын
Fabulous video, hats off!
@randalltucker9343
Жыл бұрын
Very nicely done, sir! Great video!
@_cran
9 ай бұрын
I know you mostly do calc but can you make a video about fourier series/transform-inverse transform and a video about laplace transform-inverse transform? It'd be pretty educating I think since I just know the logic of it's graph I know it's formula but I don't understand how or why it works to just integrate something with e^-ikx then re-integrate it with e^ikx shapes the function in a different way
@petersamantharadisich6095
Жыл бұрын
it might be easier to simply start with that definition of e and expand in a power series e^h = lim_n (1+h+h^2/2+...+h^n/n!) then subtract 1 e^h - 1 = lim_n (h+h^2/2+...h^n/n!) then divide by h (e^h - 1)/h= lim_n (h+h^2/2+...h^n/n!)/h = lim_n (1+h+h^2/2+...h^(n-1)/n!) then take limit with respect to h (limit is 1 and doesn't depend on n), then with respect to n (still 1)
@PrimeNewtons
Жыл бұрын
I agree. I wanted to stay within knowledge from precalculus and highlight that manipulation I showed.
@znhait
Жыл бұрын
This is circular reasoning. You just gave the Maclaurin series for e^x, which is obtained by finding the derivative of e^x. If someone is finding derivatives from first principle, the assumption is that no result that includes the derivative--other than the definition itself--can be used.
@petersamantharadisich6095
Жыл бұрын
@@znhait I don't think it is, as you can derive the power series by expanding the definition used in the video... e^x=lim_n(1+x/n)^n = lim_n{sum_j (x/n)^j × n!/[j!(n-j)!]} = lim_n{sum_j x^j/j! × [n/n][(n-1)/n]...[(n-j+1)/n]} = lim_n{sum_j x^j/j! × [1][1-1/n]...[1-(j-1)/n]} = lim_n {sum_j x^j/j!} × lim_n{[1][1-1/n]...[1-(j-1)/n]} = lim_n {sum_j x^j/j!} The above does not refer to derivatives of e^x, there is no need to use circular reasoning to get the result this way.
@znhait
Жыл бұрын
This is excellent work. I'm wondering if there isn't an easier way...or just a more obvious to come up with this limit. Otherwise, the definition of e could have been used a lot earlier.
@PrimeNewtons
Жыл бұрын
Great point!
@masoudhabibi700
Жыл бұрын
Thank for one more time.... master
@tfdtfdtfd
2 жыл бұрын
Excellent video avoiding the unelegant definition of e as the "eh-1" limit......we should probably add a few technical details about the existence of limits when you split into products, ratios, swap order of ln and lim.....these generally hold true here due to continuity
@PrimeNewtons
2 жыл бұрын
Thanks for the extra notes. Appreciated!
@barthennin6088
Жыл бұрын
It appears to be a circular argument. ln(e^x)=x and e^ln(x)=x
@PrimeNewtons
Жыл бұрын
Lol. That's what a lawyer would say. In mathematics, they are called inverse functions.
@punditgi
Жыл бұрын
My first principle is to always watch Prime Newtons! 🥰
@yigitrefikguzelses291
Жыл бұрын
When we are dealing with lim n->0 1/(ln(1+n)^(1/n) isn't this expression undefined because we have 1/n in the expression. I will be so happy if you can help me
@PrimeNewtons
Жыл бұрын
n is not 0 yet. We are just approaching 0. So the function is not undefined and you should not plug in zero into the function because then it will be erratic. Try sketching that in desmos and see what happens as you approach zero. 😉
@yigitrefikguzelses291
Жыл бұрын
@@PrimeNewtons yeah its say approxirametly 2.718 so it's e but aren't we getting different result while approching from negative infinity,(by the way thank you for your respond)
@muzza881
20 күн бұрын
I like to use the series expansion of exp(x) for this. Then exp(x+h) = 1+(x+h)+(x+h)^2/2! +........... Exp(x+h)-exp(h) term by term gives 1-1 + x+h-x + 0.5(x^2+2hx+h^2-x^2) + ........ Subtracting, dividing by h, and taking the limit gives us back exp(x). I suppose you can claim that the definition of the Taylor series already used derivatives to all orders of exp(x).
@Aferz
Жыл бұрын
Thank you SOOOOOO MUCH! You made me understand it and now I feel so good and so YEEEEEES YEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEES
@PrimeNewtons
Жыл бұрын
❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️
@JessicaShaw-ym4vc
8 ай бұрын
Hi! where does the definition of e in terms of n come from? thank you. your video was great :)
@dr.rahulgupta7573
Жыл бұрын
Sir. Can we use the definition of e^h to simplify ( e^h --1)/h and then take the limit ?
@PrimeNewtons
Жыл бұрын
Certainly. That would be highly recommended.
@dr.rahulgupta7573
Жыл бұрын
@@PrimeNewtons Yes Sir .
@Bob-sq7ev
6 ай бұрын
Thank you sir this helped me a lot ❤❤❤
@shcottam
Жыл бұрын
Dude, this is pretty sick
@paulwood3460
5 ай бұрын
Excellent proof. 👏👏👏👍👍 just one criticism..before starting the the proof of derivative e^x just state the fact that (lim n->0 (1+n)^1/n) = e Mathematics is simply wonderful.
@robertveith6383
3 ай бұрын
The exponent, 1/n, must be inside grouping symbols: (1 + n)^(1/n)
@paulwood3460
3 ай бұрын
@@robertveith6383 surely you mean (1+n)^1/n 😀
@馬瑞基
2 жыл бұрын
It is so helpful
@sergiolucas38
Жыл бұрын
Great video, you're very didactic and your letters are quite pretty as well, thank you :)
@PrimeNewtons
Жыл бұрын
Thank you
@K-drama-LegendKing
2 жыл бұрын
thanks for not using circular logic this makes so much sense the video is amazing, i would love to check your other videos although i know the the derivatives but the way you explained this one im excited to see the other derivatives
@JulesMoyaert_photo
10 ай бұрын
Nice demo!
@kaboflotv6455
Жыл бұрын
What about y=sin(×+1) from first differentiation??kindly asking
@PrimeNewtons
Жыл бұрын
I have to a video for sin x. Use the same idea.
@PrimeNewtons
Жыл бұрын
Same exact process. You'll get cos(x+1)
@ukidding
9 ай бұрын
you have v nice writing
@PrimeNewtons
9 ай бұрын
Thanks a lot 😊
@ΛαζαροςΙωαννιδης-φ5υ
6 ай бұрын
Bravo. Perfect.
@12388696
2 жыл бұрын
Well done
@komalshah1535
11 ай бұрын
Fantastic sir!
@patelharsh5133
3 жыл бұрын
Thanks sir
@geraldomelo2751
9 ай бұрын
The l'hopital theorem can also be applied.
@durjoysaha2896
4 ай бұрын
That helps a lot❤
@Rayglobster
Жыл бұрын
This is perfect
@the_n_ecromancer
6 ай бұрын
"you see that? That makes life a lot easier"😂😂😂
@hypothesisnyc916
2 жыл бұрын
Your teaching style is great but it bugs me that you're using implication symbols as though they are equal signs. For students to know the difference between "equals" and "implies" makes a big difference in their understanding of proofs.
@PrimeNewtons
2 жыл бұрын
I completely agree. I promise to never do that again. Could you suggest a replacement for doing my transition without using the implication symbol.
@TofaraRungano
9 ай бұрын
Culculas simplified ❤
@Pauladam2216
3 жыл бұрын
Nice
@nievalesterloydp.7399
Жыл бұрын
Ang angas
@CarolineSikamoi-rh7iv
Жыл бұрын
Encourage though small writings make them more clear atleast
@atri5280
2 жыл бұрын
ॐनमःशिवाय 🙏
@reddottgamer3047
2 жыл бұрын
Finnally earth become a livable place.
@ThenSaidHeUntoThem
2 жыл бұрын
You are hilarious 😂
@anestismoutafidis4575
9 ай бұрын
It stays as it is= e^x, except for x we put numbers ( N○ - C)
@mazenzidieh
10 ай бұрын
Thanks alot
@sochegeorge7962
Жыл бұрын
Can someone please explain the move at 9:32
@sochegeorge7962
Жыл бұрын
Should have added if n = 23, (1/23)*ln(24) is NOT equal to Ln(24)^(1/23)
@ThenSaidHeUntoThem
3 жыл бұрын
Coool!
@shivankargupta6675
Жыл бұрын
😍😍😍😍😍
@petechen794
10 ай бұрын
It's not difficult. You may use the definition of derivative to do it. You may also do it by using ln .
@СергейКовалев-т1д6м
5 ай бұрын
👍👍
@justinnwachukwu2054
Жыл бұрын
Write your number on the board. I appreciated your teaching style
@PrimeNewtons
Жыл бұрын
My guy, I no fit write my number for blackboard na! Wetin be dat?
@GiftMlinde
2 ай бұрын
Eeeee sir ❤❤❤❤
@fardowsakhalif6669
Жыл бұрын
M.Allah
@fardowsakhalif6669
Жыл бұрын
Shugran
@clemensvorbauer1183
10 ай бұрын
you could have derived the rule of differentiating x^n from first principles easily, and than differentiate the definition of the exp-function, the power-series….
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