You know its about to get real when he starts using the blue pen (-:

@blackpenredpen

6 жыл бұрын

yup, that's right!

@ciherrera

5 жыл бұрын

Somewhat relevant xkcd: xkcd.com/849/

@Peter_1986

4 жыл бұрын

He has also used a purple pen a few times.

@leviackerman6090

3 жыл бұрын

😂😂😂😂😂😂😂😂

@in-ty8vb

3 жыл бұрын

Multiple Colour Pen

I have graduated 3 months ago, at the start of the calculus class 2 years ago i hated calculus but here i am, loving calculus and enjoying every second of your awesome videos.

@blackpenredpen

6 жыл бұрын

Alex Ramyeon thank you!!!!!!

@tintinfan007

Жыл бұрын

Honestly speaking calculus is more fun than GTA and all other video games.

@ct---cp8li

11 ай бұрын

@@blackpenredpen my way docs.google.com/document/d/e/2PACX-1vQ0SB1cs5gR0S17zmIhfFuQqmhGsw8_jn_QoL1n6AjI26wsu2bOPIxzCrw1D0SK-fCca1FUR-xAQ-gI/pub

@aaxel_dz

7 ай бұрын

@@tintinfan007 you're probably speaking about some random mobile gta spinoff

@climbeverest

7 ай бұрын

I love the way he teaches

8:11 Talking to your GF

@williamhutsch851

5 жыл бұрын

under rated comment

@jacobious1537

5 жыл бұрын

Perfect

@thejiminator8816

5 жыл бұрын

Lol

@phatkin

5 жыл бұрын

ayyy

@future62

5 жыл бұрын

Very good lmao

8:25 my brain to me after a test

@banana6108

3 жыл бұрын

Underrated

@hopelessdigger

3 жыл бұрын

Lol

@user-pd4wz1oo3x

2 жыл бұрын

Lol

@lucasscoz6090

2 жыл бұрын

lol

@prasannashrestha3519

2 жыл бұрын

lol

10:43 I really love the satisfaction I get when my mind snaps and know how the demostration continues before the video. Great video!

@vvvss-cx1vd

Жыл бұрын

Clicked at around 7:50 for me, so satisfying

@BradleyG01

Жыл бұрын

was about to cmment that same thing! It's such a great feeling

How do we know ln(x) is a logarithm? I once had a professor “define” ln(x) as a function whose derivative is 1/x. He then proceeded to show the ln(x) is indeed a logarithm, and it has the base e. I’d like to see this again. It was very inspiring, but I have forgotten how it was done.

@blackpenredpen

4 жыл бұрын

Are you asking how to prove the properties based on that definition? If so, I have a video here kzread.info/dash/bejne/Znhhr5eqcsLSZs4.html

@tckgkljgfl7958

3 жыл бұрын

@hobo doc id be happy to receive those pages on scrubster@gmx.de

@lewisbotterill4948

3 жыл бұрын

I was taught that ln(x) is by definition, log base e of x. The term ln itself means the natural logarithm.

@cellcomsanggau424

2 жыл бұрын

@@lewisbotterill4948 look

@lewisbotterill4948

2 жыл бұрын

@@cellcomsanggau424 ?

Another proof using parametric equation: x = e^t y = t dx/dt = e^t dy/dt = 1 (dy/dt)/(dx/dt) = dy/dx = 1/e^t = 1/x

@rajendramisir3530

5 жыл бұрын

Wonder proof buddy! Three different proofs: Limits, implicit differentiation and parametric equations.

@rajendramisir3530

5 жыл бұрын

Wonderful proof buddy! Three different proofs: Using parametric equations, limits and implicit differentiation.

@DaveJ6515

4 жыл бұрын

Just brilliant. Congratulations, I’m going to teach this one tomorrow

@pradipgiri8321

4 жыл бұрын

nicely done

@RamsLiff

3 жыл бұрын

For any log , 1/x .ln a, a its the base of the log , If a = e, the derivative is 1/x I did a general proof

I really enjoyed your last few videos, and I am glad you're back to uploading more videos containing your explanations

Just watched it again as there were a few things I wasn’t sure of. I really liked it when he explained one trick to use was because the natural log is a continuous function, and the limit of a continuous function is a continuous function of the limit, you can move the limit inside the parentheses to simplify things. Cool stuff.

I have always wanted a more detailed explanation of this result. This is the best I’ve seen on the subject. Considering things like Euler’s identity and the quantum wave equation and other uses of the exponential function, it seems to me it’s the most useful of all the special functions.

Wonderful videos. It is a long time ago that I studied complex variables, differential and integral calculus and algebra. So it is great fun watching this guy do with ease what most of us struggled with when learning the basic elements of these important mathematical techniques. I can generally follow him right to the end once I see where he headed. The mathematical manipulations seem to be firmly rooted in my brain. The algorithms he applies for problem solving are much less so.

Elegant proofs for the derivative of ln(x). I like the intelligent and creative ways you used to develop and establish your proofs. Thanks.

Great video man! I feel like you've made me so much smarter; this time I was actually able to see ahead a little bit, that the argument of ln would end up being e^1/x (this was around when you brought the derivative into the u world)

You are my new favorite high school math teacher. In my AP calculus class, we were never taught how to derive this. Only taught to memorize that d/dx ln(x) = 1/x

Well done guy! You sort it out! Keep it up! Go always deep n in every detail to enlightening. Again you've done it!

Another way : exp(ln(x)) = x Derivative of both sides : ln(x)' * exp(ln(x)) = 1 Replace exp(ln(x)) by x and divide the whole equation by it : ln(x)' = 1/x

@MiroslavOstapenko

10 ай бұрын

wow!

@TheLifeLaVita

8 ай бұрын

it's literally in the video

Its a shame we dont get teached this stuff in school but are just supposed to remember f'(x)=1/x of F(x)=ln(x)

@ChaosPod

6 жыл бұрын

I remember my school teaching us a variation of the 2nd method, namely y = ln x => e^y = x Therefore dx/dy = e^y dy/dx = 1/(dx/dy) = 1/e^y = 1/x

@Witiok1992

6 жыл бұрын

FF same situation(((

@ZZaarraakkii

5 жыл бұрын

Of f(x)=ln(x). Capital f often implies integration. Especially because integrated function is defined by it F'(x)=f(x) then you are ok.

@sjoerdo6988

5 жыл бұрын

they told us: e^ln(x)=x diferentiating gives: e^ln(x)*d/dx(ln(x))=1 d/dx(ln(x))=1/e^ln(x)=1/x

@znhait

5 жыл бұрын

This is just the application of the first principle definition of the derivative. You know how to do limits and should be well versed in algebra manipulation. It's not a big leap to do this problem. This is the sort of exercise a student should do away from school.

Thank YOU so much for sharing your beautiful smile and passion!! It makes me so much more excited to learn and genuinely happy :))

Oh my god you are incredible! I learned a thing or two because of you! Loved it ❤️

So clear explanation, Greatest Math Teacher in the WORLD, Thank You Sir!.

Just found your channel. Thanks for creating this content and keep up the good work.

This reminds me of when I was a COBOL programmer, we would have discussions about whether you could have positive zero and negative zero. This was because the sign of a number was contained in the units digit. So, when comparing numbers it was important to take this into account. But I would say to my colleagues that zero was neither positive nor negative, it was separate from other numbers.

this math professor dripping out with tha preme jacket

@valiok9880

4 жыл бұрын

Gavin Burns lmaooo

Absolutely beautiful. Great explanations! Thank you.

I've always been told that the derivative rule for f'(x) of ln(x) has always been 1/x but I've never understood how that was proven. Thank you for the explanation.

@carultch

10 ай бұрын

There's usually one of these proofs for it somewhere in the textbook. Since the teacher probably sees proving them as reinventing the wheel, and not necessary to understand the subject, they probably just skip showing why these derivative rules work.

Dear friend, you are not only genius but you a great guru (teacher). My regards - Sudarshan🙏

It's so beautiful ♥ Great explanation!

This was so intertwining I was guessing what to do and when he showed what to do it made sense feels amazing

dayuumm now that's impressive, finding the derivative of ln(x) using the standard definition of a derivative

You can also use the formula for inverse derivatives. This is how I did it: Let g(x) = the inverse of f(x) g’(x) = 1/(f’(g(x)) Let f(x) = e^x Therefore f’(x) = e^x & g(x) = lnx g’(x) = 1/(e^lnx) g’(x) = 1/x Therefore the derivative of lnx is 1/x. To prove the formula I used, you can let g(x) = inverse of f(x) So, x = f(g(x)) Differentiating both sides, you get: 1 = f’(g(x))*g’(x) g’(x) = 1/(f’(g(x))

@xnqmap

Жыл бұрын

It basically what he does from 13:00, without explicitly using the formula for the derivative of a reciprocal function.

Thank you, you are the best explaining ♥️

I wonder if there is a numerical analysis class he teaches. This guy is a good teacher.

The second lim going into the continues function was so eye opening and satisfying

blackpenredpen could you solve the non elementary integral of x^x. You did the (easier) derivative so please do the difficult integral or let Payem do it

@angelmendez-rivera351

5 жыл бұрын

Ahsoka Tano How is he suppose to solve it if it is non-elementary? Do you understand what solving an integral is? And do you understand what non-elementary is?

@zachcate7102

5 жыл бұрын

Angel Mendez-Rivera ima be real with you that made no sense

@nicememe8608

4 жыл бұрын

Zach Cate if an integral is non-elementary, by definition, that means you cannot solve it. It will be defined by a special function. For example, the fresnel integral

@hassanakhtar7874

4 жыл бұрын

Okay for anyone that is confused this is a matter of pedanticism. "Solving an integral" technically refers to definite integrals. The original comment probably just wants the indefinite integral and is using the word "solve" to mean "to do" as in ordinary english. Again, all a matter of mathematical vs normal language.

Thank you for this awesome video! Also, I could make the proof shorter by using equivalence "ln(1 + h/x) ~ h/x" on the 2nd step in your proof

@dudono1744

2 жыл бұрын

this approximation is based on derivative of ln(x)

Dang, when he finally pulled out the e term, I got super excited. Nice job!

I love u-sub when doing algebra and calculus. SO useful.

YOU ARE PHENOMENON!!!!!

Smart moves and thank you. To avoid confusion in approach 1 instead of twice using u I will use U and then w.

جميل ورائع ومميز ما يقوم به هذا الشاب،،، فعلا عقليه فذه،، 🌹🌹🌹

I love you, plain and simple.

This mad lad really just used the limit definition. Can we get this guy a medal?

Very elegant description of this important derivative

Such a great video on this!

You can do this in two ways. You can use the integral definition of log(c) and use the fundamental theorem of calculus or you can note that log(x) is the inverse function of exp(x), and just use the expression for differentiating the inverse function.

How easily he changes markers is amazing to watch

Thanks i like you so much, maths is magic ♥️. I try to find this by focus on the definition of a function wich is derivating if this limite was not infinity and i encounter a lot of problème by not knowing this definition of e and also "the limit of a continuous function is the function of the limit. Thanks a lot ♥️ Sorry i dont speak english very well but i learned more and more each days

Hey , I recently started reading Thomas calculus and found that lnx was actually defined as definite integral of 1/t from 1 to x. So i think a proof is not needed stating the definition is enough. Anyway hats off to the great content

@carultch

10 ай бұрын

How it is defined, really depends on who you ask. Historically, natural log was discovered before the number e, and it was defined as this integral. But in modern times, we usually define it as the inverse of e^x, and define e^x as the special case of the exponential where it is its own derivative. The modern definition is much more useful, to learn what logs are for the first time. These two definitions are internally consistent, but you need to start with one to prove the other.

THANK YOU!!! All other videos I found only explained how you used the derivative not actually showing proof on why it’s 1/x

Wonderful work!

Finally, since the basketball secret has been revealed I can find some sleep!

@blackpenredpen

6 жыл бұрын

Marian P. Gajda in fact, in was in that previous video as well, just allllll the way at the end.

@derekanderson1214

6 жыл бұрын

I live close to where you recorded that basketball video! I was pleasantly surprised when I saw that

@blackpenredpen

6 жыл бұрын

Derek Anderson Are you serious??? How did u even recognize that place!!!

@aashsyed1277

3 жыл бұрын

@@blackpenredpen COINCIDENCE?

@aashsyed1277

3 жыл бұрын

@@blackpenredpen it is possible, but very unlikely

Excellent, as usual!

I watch your videos for inspiration and help as I just started year 7

Awesome explanation

I love these type of people on KZread

I think it could have been made a bit more clear at 3:29 that the 1/h exponent is supposed to be evaluated for (1+h/x) before the log is taken. (But I still got the point.)

I just wanted to say, that for some reason, LOGb(X)=ln(X)/ln(b) has always been my favorite relationship in "Logarithmic Functions" and THANKS for the bonus at the end!!!

@jamesfortune243

2 жыл бұрын

X = b ^ logb(x), then take logd of both sides and bring the exponent down. Then solve for logb(x).

thanks brother for clear information ❤🤗🤗😎😎

Thanks bro. Awesomeness

you’re so awesome!!

That was pretty cool!

I have a fourth proof: If we differentiate e^ln x, instead of resulting in x, we use the chen lu, where u = ln(x). That results in e^(ln x) * du/dx. However, if we use the power rule, it results in 1. Therefore, x * du/dx = 1. We solve for du/dx = 1/x.

Back when I learned this we defined the logarithm function in terms of the integral 1/x dx, then proved that this function had the properties expected of a logarithm.

@luisvasquez-ib1dk

Жыл бұрын

CIERTO BRO YO TAMBIEN LO APRENDI AL REVES,QUE EL LOGARITMO SE DEFINE JUSTO POR LA INTEGRAL DE 1/X

That was beautiful!

Thank You so much sir!😇

Amazing job man

This was so cool!

The limit definition of the derivative of ln(x) is a nice one!

12:05 when I saw this, I was like... OMG I just realized what the hell I've been watching for the past 12 minutes... I was more intrigued by what he was able to do in terms of modifying the formulae, but then noticed he brought it down to 1/x, I love this guy.

The most impressive thing about these videos is not the math, it's his ability to write with 2 or 3 markers in the same hand while holding them all at the same time. And that his writing is still legible while he does it. I can barely read my own handwriting when i write with just 1 pencil

@CliffSedge-nu5fv

7 ай бұрын

And hold a microphone in the other hand. Might as well start juggling at that point.

This is so awesome.

6:30 Hum. Ah. But when we say limit(h->0) that implies in any direction right ? As we work with real numbers we can have h 0 and both directional limits (or whatever the proper name for that is) must give the same result for the derivative to exist. But when we substitute for h->infinity, we only check the side h>0, right ? So shouldn't we also substitute u=-1/t and verify that we have the same result ? Or else prove that the derivative must exists in which case only one side is enough to get the value.

To differentiate ln(x) I use this trick: 1 = 1 1 = d/dx x 1 = d/dx [e^(ln(x))] 1 = e^(ln(x)) * d/dx(ln(x)) d/dx(ln(x)) = 1 / [e^(ln(x))] d/dx(ln(x)) = 1/x This also works for all inverse functions like arcsin(x), arcos(x) & arctan(x).

so beautiful !

youre my inspiration

well done professor

I like all the math problem and solutions 👍👍

Thank you so much sir.

Well done!

such a long proof but very well thought out. I was definitely doing a shorter proof for my test (luckily, not sure if I could survive writing this for my test.. lol). Dloga(x)=1/x*ln(a) D(log(e^x))=1/xlne=1/xloge(e)=1/x*1=1/x but of course mine is already making assumptions (that derivative of loga(x)=1/x*ln(a)) instead of figuring it out with definition of e. Great work, definitely I learned something.

Love the second proof of lnx's derivative

I like your channel, its content and overall disposition (subscribed long back). I would like to mentiom that a lot of times you seem to show some very simple or basic algebraic manupilation in great detail as if you are showing that to some beginner who is not very bright. I request you to be consistent in knowledge density (idk how to describe thos) throughout the vdo and spread your time evenly on the topics and ponder over stuff which really calls for it. In this vdo, time spent on definition of e with t to u is probably 6 times than necessary, my personal feeling. Lastly, as I like this channel, I complained. If I was indifferent, I wouldn't have cared.

it's always cool seeing derivations for things you learned without the reasoning behind them

wow! thank's a lot for the explanation, now i know why it's 1/x :)

Awesome man

Nice piece of Mathematics.

Proving this was actually a question on one of our calc exams

Which was proven first, the derivative of e^x or that of ln x?

Mst ...

16:43 Yeah! It even works for e: ln(e)=1 so you get back the 1/x :)

Very well explained as usual, only one thing: I ask my students to avoid “canceling ln with e”; I want them to say that log of a power with the same base is the exponent.

@stewartzayat7526

4 жыл бұрын

I think that's just a linguistic thing. As long as your students know _why_ it works, I don't think it matters what they say

@DaveJ6515

4 жыл бұрын

@@stewartzayat7526 Since that is the definition of a log, I prefer my students to repeat it as frequently as possible: it's the best way to capture it completely. It's part of my campaign against voodoo maths: you know, strange things like quantities that change their sign while flying over the equal sign and all that. An easy way to forget that there are equivalence principles behind that, and no flying stuff. Also: linguistics is a central part of our learning processes: our first impact with new stuff is via a language, so it makes lot of difference, imho.

@diegocabrales

Жыл бұрын

Logarithm is the inverse function of exponentiation and viceversa, that's why log_a(a^x) = x and a^(log_a(x)) = x. I would prefer to say this rather than what you have written here (that includes the equivalent of what you have said for explaining that a^(log_a(x)) = x).

@DaveJ6515

Жыл бұрын

@@diegocabrales and of course you would be right, but my 36 years of experience teaching maths make me say that your students would benefit less from that explanation.

Very satisfying and pretty!!!

At the third step you could have broken the fraction into 1+h/x and then divided and multiplied the base h with x instead of using it is as power then you would have got 1/x lim h->0 ln(1+h/x) divided by h/x and then by using the limit you could’ve simply got 1/x

Thank you so much.

i think to explain why you can shoot the limit into a continous function you would need into to analysis.

This is beautiful

A most elegant solution to d/dx Ln(x)...I didn't imagine it would take 3 substitutions.

the first definition are amazing

I literally love this channel holy shit

cool. thanks you, sir