Wow this man used to be my teacher. He's over 90 years old now and I'm so glad to see that his lessons are still being appreciated by new generations of students.
You are still teaching at the age of 94. It means that you are so strong and have the spirit of teacher. I was surprised and really appreciate you. I hope you have happiness, long age and good health. As I am only a student who loves teaching now, I have encouragement to continue doing my channel to publish educational knowledge. It is a wonderful thing.
Esse vídeo me fez chorar, tocou meu coração de verdade é tão emocionante e bom ver uma pessoa fazendo o que ama. O senhor é incrível! Só estamos aqui por um professor que nos ensinou e devemos tudo a vocês!
I've come from the BlackPenRedPen channel, and I must say, you, sir, have blessed my day with such a beautiful, detailed and comprehensive explanation of this problem! Please continue teaching with such grace and passion, there are people who really appreciate it 😁
This guy is great. Nothing limits him from helping the next generation. He is a good role model. Soon I’ll be starting calculus, and hopefully I can help others too. Thank you for your work!
@@maalikserebryakov Yeah cause finding joy in teaching people calculus & physics online is magically evidence (??) for wasting one’s life (??) for “cope approval” (??). You somehow found an assumption that people teaching math automatically means they’re wasting their time trying to get societal approval (for ?). I would love for you to explain how you came to this utterly baseless and senseless conclusion, if you can (with actual proof).
My mind was blown when I saw where you were going with this solution! My first thought would be to solve for f(x) then take the derivative, but that would’ve been a lot of extra work. Brilliantly done!
It’s actually not too bad f(x) is pretty nice. From number 3 we multiply by f(x)+x and get (f(x))^2 + xf(x) = xf(x) + x^2 + 1 Cancel xf(x) and we get (f(x))^2 = x^2 + 1 so we simply have f(x) = sqrt(x^2 + 1) for positive x and f(x) = -sqrt(x^2 + 1) for negative x Using the power and chain rules we get for positive x like 99 f’(x) = (1/2)(1/sqrt(x^2+1))(2x) f’(x) = x/(sqrt(x^2+1)) We then get a very nice cancelation f(x)f’(x) = (xsqrt(x^2+1))/(sqrt(x^2+1)) f(x)f’(x) = x We can see that this also holds true for negative x. So for any positive or negative x the answer is simply the input. (Note our original function has an issue at x = 0 so we can’t plug in 0)
Im really happy that i got introduced to your channel and love to see people enjoying mathematics even at that age and that the love of them didnt leave you with desire to teach them to other who seek the knowledge
Clear to follow, and done excellently. Thank you for making videos and inspiring others to do math!❤ Edit: Props to blackpenredpen for seeing his video and sharing it with others, and I hope it makes it so that Feng can get more students. Also find it crazy that blackpenredpen saw Feng’s videos right after I did because I watch blackpenredpen all the time and just find it strange.
it's tricks like these that make me like maths thank you sir, your way of teaching also makes the material seem way more straightforward, like there's no room for agonizing over the next step
At first, I thought you would first try to find f(x). But the way you manipulated the problem and used f(x)+x in denominator literally amazed me and provided me a new way of thinking for problems which looks complicated. Thank you so much
I want to let you know that you’ve helped students from all over the world. Thank you for continuing to share your passion with all of us🥳 Math wasn’t always my favorite subject, but i’ve grown to appreciate the subject. it’s fascinating-and your video is proof of that. I really enjoyed the lesson! Thank you! 😊
I want everyone to know I saw this in my recommended without even having interacted with the link on bprp's video yet, so the algorithm has been working on pushing this to the top!
![[Physics] - Dynamics Problem | Friction | Force | Newton Law | #newtonlawofmotion #physicsproblems](http://i.ytimg.com/vi/v_urpDHbbUg/mqdefault.jpg)
This is true greatness!
Thank you for introducing him to us ❤
yesss
❤❤❤
thx bprp
bprp in 50 years if he lives long enough.
Wow this man used to be my teacher. He's over 90 years old now and I'm so glad to see that his lessons are still being appreciated by new generations of students.
Dear Andy:
I still remember you. Please chat with me about how you are doing.
Very pleased to see your message.
Yours truly
S. Feng
Single take! No edits! That’s what I’m talking about! 👏👏👏
Oi
aperte meu ovo esquerdo 3 vezes consecutivas
yes old school stil alive
When u know what ur doing no second chances needed 🤌🏼
kkkkkk esse cara também conhece o bprp
An intimidating problem elegantly solved!
A teacher who isn't afraid of showing all the steps. Thank you for teaching me. 😀
You are still teaching at the age of 94. It means that you are so strong and have the spirit of teacher. I was surprised and really appreciate you. I hope you have happiness, long age and good health.
As I am only a student who loves teaching now, I have encouragement to continue doing my channel to publish educational knowledge. It is a wonderful thing.
Wish you success!
@@water6133 Thank you so much.🙏
My best wishes ❤️
@@abhisheksoni9774 Thank you so much.🙏 You, too.
It is really impressive.
That smile at the end 18:30, simply precious
Thanks a lot grandmaster.
you can see the shaking of this fingers in the letters but he is still teaching with passion! amazing
The way he has written the explanation of each step is commendable, most of the modern teachers don't do this.
Sir with due respect ,I respect your dedication towards education, you're teaching at 94!! , I'd be gald to be your student.
You can't because you are so very stupid
Wonderfully solved! The moment you made the right side of the equation definite using [f(x) +x] as the denominator genuinely amazed me.
Awesome video!! Thank you for sharing this!
Also, Steve from BlackPenRedPen sends his regards (and viewers)
His name is Steve? Cool name
lol he is steve? cool
@@justsaadunoyeah1234yes bprp’s name is Steve Chow
One of the most heartwarming things I have seen all year
Same here. It was difficult to focus because of it.
Esse vídeo me fez chorar, tocou meu coração de verdade é tão emocionante e bom ver uma pessoa fazendo o que ama. O senhor é incrível! Só estamos aqui por um professor que nos ensinou e devemos tudo a vocês!
Resumiu bem o que todos deveriam sentir no coração.
Perfeito comentario
This is one of the clearest and cleanest work I’ve ever seen…
Beautifully solved. ❤️
It was indeed.
True meaninv of life
I was not expecting the elegant reveal at the end! The build-up to the solution was worth it and was easy to follow.
Thank you sir for showing this cool, intersting problem.
I've come from the BlackPenRedPen channel, and I must say, you, sir, have blessed my day with such a beautiful, detailed and comprehensive explanation of this problem! Please continue teaching with such grace and passion, there are people who really appreciate it 😁
Hey Mr. Feng, you are inspiring amount of students and teachers in Brazil!!! Congratulations!!!
This guy is great. Nothing limits him from helping the next generation. He is a good role model. Soon I’ll be starting calculus, and hopefully I can help others too. Thank you for your work!
He wasted his time to get cope approval like this.
Approval from society is a poison that enslaves.
@@maalikserebryakovif teaching others is truly enjoyable to him how can you call him a slave for doing what he loves?
@@maalikserebryakov Yeah cause finding joy in teaching people calculus & physics online is magically evidence (??) for wasting one’s life (??) for “cope approval” (??). You somehow found an assumption that people teaching math automatically means they’re wasting their time trying to get societal approval (for ?).
I would love for you to explain how you came to this utterly baseless and senseless conclusion, if you can (with actual proof).
What an ingenious solution to a problem that seems difficult at first sight.
My mind was blown when I saw where you were going with this solution! My first thought would be to solve for f(x) then take the derivative, but that would’ve been a lot of extra work. Brilliantly done!
It’s actually not too bad f(x) is pretty nice. From number 3 we multiply by f(x)+x and get
(f(x))^2 + xf(x) = xf(x) + x^2 + 1
Cancel xf(x) and we get
(f(x))^2 = x^2 + 1 so we simply have
f(x) = sqrt(x^2 + 1) for positive x and
f(x) = -sqrt(x^2 + 1) for negative x
Using the power and chain rules we get for positive x like 99
f’(x) = (1/2)(1/sqrt(x^2+1))(2x)
f’(x) = x/(sqrt(x^2+1))
We then get a very nice cancelation
f(x)f’(x) = (xsqrt(x^2+1))/(sqrt(x^2+1))
f(x)f’(x) = x
We can see that this also holds true for negative x. So for any positive or negative x the answer is simply the input. (Note our original function has an issue at x = 0 so we can’t plug in 0)
Great!
Such interesting problem and excellent solution!
such an amazing question..thank u for sharing Sir❤🙏
Im really happy that i got introduced to your channel and love to see people enjoying mathematics even at that age and that the love of them didnt leave you with desire to teach them to other who seek the knowledge
You're amazing sir
Amazing mathematics teacher solving an amazing mathematics problem.
Its really a good way to solve those kind of problems ,thank you teacher
Teacher, I am humbled by your generosity. Thank you for the lesson.
Elegant and ingenious! Thank you sir
Clear to follow, and done excellently. Thank you for making videos and inspiring others to do math!❤ Edit: Props to blackpenredpen for seeing his video and sharing it with others, and I hope it makes it so that Feng can get more students. Also find it crazy that blackpenredpen saw Feng’s videos right after I did because I watch blackpenredpen all the time and just find it strange.
Such a nice equation with a very satisfying solution.
Support from Japan! This is great content, please keep it up!! 応援してます！
Beautiful explaination sir!
Great explication Mr.Teacher 🫡🫡
Dear Sir, Thank you for your problem and explanation. Keep up the good work!
Had no idea how would you use derivatives for this problem, is a really nice solution! Thanks a lot
Beautiful answer, and master manipulation of established rules
Dedication at its peak ❤️🔥
Amazing how he shows every step, makes everything super clear and simple. He is definitely a great teacher
I liked the way an intimidating problem is solved so trickyly by a senior professor. Thanks a lot for the video.
Thank you Sir for your great explanation.🙏🙏😊
Wow nicely done! Thank you for the video.
You are an absolute blessing. Thank you so much for your contributions and your love of teaching!
I'm from Brazil. I don't now speaking english, but I understand your lesson. Thank you!!
Amazing🎉
Thank you for sharing your knowledge! 😊
it's tricks like these that make me like maths
thank you sir, your way of teaching also makes the material seem way more straightforward, like there's no room for agonizing over the next step
The dedication and passion that we can see in your teachings are so inspiring and admirable!!!
Thank you very much sir, you are a very good teacher and a smart mathmatician
Amazing video ☺️ thank you so much for sharing your knowledge!
Recall my memory when I got this problem in junior high school math competition. Thank you sir! Great explanation!
I am going to watch this video at least 5 times. Not only to understand the problem and solution thoroughly, but also his way of teaching.
You said too nice. I am not that good.
Thank you so much.
A true inspiration for us all youngins... Keep trekkin buddy...❤❤❤
great solution ❤️
Ok, this explanation/answer is fantastic. Thank you sir.
Such an awesome explanation and solution, sir. Thank you so much !
Incredible, thanks Sir 🎉
Brilliant result. Thank you for this example. 😊
Very interesting. Thank you Professor for the resolution.
Amazing. We love you, sir! ❤❤❤
Thank you for sharing your passion with us all!
Thank you for sharing your gifts and enriching the world 🥹🥰
Just came here from bprp. Can't wait to see every video on this channel. Much respect!
Thank you, Professor, for this great explanation :)
Great exercise!
At first, I thought you would first try to find f(x). But the way you manipulated the problem and used f(x)+x in denominator literally amazed me and provided me a new way of thinking for problems which looks complicated. Thank you so much
Hat's off to u sir ...love from Hyderabad,India... Witnessed a genius today
This is a calculus mastermind, thank you very much good sir
Very well explained. Thank you!
Such an intuitive approach thank you so much!
Amazing that you show how to do it step by step and stating clearly how you get the next step from.Appreciate the video😊
Found this channel via Blackpenredpen. Mind-blown by the process of solving and subscribed afterwards. Thank you sir.
Great content
'Chapeau bas' grandmaster. Detailed and ultra clear explanation.
Thank you sir for your service to the mathematical community 🎉
Thank you Sir for teaching us! It is very interesting problem to solve!
شكرا شكرا شكرا انت أفضل أستاذ واصل
Nice question. An your solution is very beatiful. Congrats 🎉🎉🎉🎉
I want to let you know that you’ve helped students from all over the world. Thank you for continuing to share your passion with all of us🥳
Math wasn’t always my favorite subject, but i’ve grown to appreciate the subject. it’s fascinating-and your video is proof of that. I really enjoyed the lesson! Thank you! 😊
Fantastic video! Thanks a lot
This was by far the most enjoyable 19 mins I've spent learning maths in in my life! liked and subscribed!
Sir, you have my respect. God bless you
Thank you very much for this awesome video❤
Amazing, Thank you sir🎉❤️
Thank you for the question, God Bless You🙏🏾
Sir you are amazing.
A true inspiration.
真的對這些終生致力於教學事業的人感到十分敬佩與感謝（重點人家還教的簡明扼要）👍
Bela aula, professor ⚘️👊🏻🇧🇷
What a sublime solution. Kudos!
Excelente… thank you teacher…
I want everyone to know I saw this in my recommended without even having interacted with the link on bprp's video yet, so the algorithm has been working on pushing this to the top!
Same
I had no idea how to solve it! sensational!
Thank you for teaching, Sir!
Nice math problem! Great method of answering!
Beautiful problem with an elegant solution! 😃
Came here from TikTok! Thank you for sharing your knowledge