To see subtitles in other languages: Click on the gear symbol under the video, then click on "subtitles." Then select the language (You may need to scroll up and down to see all the languages available). --To change subtitle appearance: Scroll to the top of the language selection window and click "options." In the options window you can, for example, choose a different font color and background color, and set the "background opacity" to 100% to help make the subtitles more readable. --To turn the subtitles "on" or "off" altogether: Click the "CC" button under the video. --If you believe that the translation in the subtitles can be improved, please send me an email.
No word to say 👌👌👌💐💐 , great job for concept clearing . Can I get more videos on maths and physics plz. If yes plz send me link and how you create this videos
In case you have not already seen them, I also uploaded several other videos in the past several days. As always, for each video that you like, you can help people find it in the TH-cam search engine by clicking the like button and writing a comment. Lots more videos are coming very soon. Thanks.
Eugene Khutoryansky As always, this leaves me open-mouthed. Even though I am studying engineering and I find deriving as simple as opening a peanut barehanded (and the simplest derivation is indeed the polynomial derivation), I couldn't imagine being able to actually VISUALIZE a polynomial derivation like this. It left me totally outsmarted. And I am so happy everytime I watch your videos because either I learn something new, or I get something I knew clarified. Only one little thing I'd like to point out: I read somebody having doubts about the effective loss of precision due to the difference between the incremented area and the "lost" area. Maybe you could have pointed out in a graphical way that the increment is infinitesimal (is it correct? I mean infinitely little) and that dx is actually the smallest increment one could ever imagine. I thought a way to show this could have been making a big zoom on the edge of the cube (or the square) and showing a very little increment over the whole volume/area, so little that not only by saying it, but by even showing it, you demonstrate how little and negligible is the increment dx (and thus the differential dy).
***** Basically every word of that applies to me. One idea I had for visualizing why the missing edges and corners don't affect the result was to show the green squares slowly narrowing until they look like sheets of paper, and have Kira say something like "As the magnitude of dx gets smaller, 3x^2dx becomes a closer and closer approximation of dy"
Adam Thornton well, actually you are wrong because 3x^2 dx IS dy with no approximation. the notation d(variable) means that we are talking about differentials. If we are approximating a quantity, we should use the limit. In particular, we should be talking of DELTA X and DELTA Y (which are differences and not differentials), whose ratio (DeltaY/DeltaX) is the incremental ratio... whose limit as DELTA X approaches 0 becomes the derivative (in this case 3x^2) with no approximation. Remember that dy and dx are infinitely small numbers, close to 0. And it is their ratio, the ratio of these two infinitely small number, which is the derivative of the function. You can't approximate a derivative, but only an incremental ratio, because the derivative is the infinite approximation of an incremental ratio :)
i genuinely thank you from the bottom on my heart this was sooo good it gave me such an intuitive sense into visualising calculus i have searched books asked all the teacher in my college and outside looked for hours online , but didn't feel satisfied ...but this is so great it doesn't leave me with a new complicated rule , the logic is so clear in your video ,instead of telling us to accept some basic rules you showed it exactly ...and also answered the question the viewer must have about the red area/vol/4d equivalent THANK YOU SO MUCH i am so glad i found your channel
You can help translate this video by adding subtitles in other languages. To add a translation, click on the following link: th-cam.com/users/timedtext_video?ref=share&v=tWnvt-8wSeA You will then be able to add translations for all the subtitles. You will also be able to provide a translation for the title of the video. Please remember to hit the submit button for both the title and for the subtitles, as they are submitted separately. Details about adding translations is available at support.google.com/youtube/answer/6054623?hl=en Thanks.
subscribed! you're a blessing! i always have an itch to visualize mathematical concepts. glad to have found it in your channel! please make more videos :D
Dan Albl Thanks. I am glad you liked it. I made this video only a few days ago, so hopefully there will still be many more people who will have the opportunity to view this. Thanks.
Eugene Khutoryansky On almost all your videos you only have a couple of dislikes. That says enough, keep doing what you are doing and after time more and more people will come to appreciate your work.
Never thought I would swear about cal in positive way, these videos are so F'en clear, watching these videos should be mandatory for any class. Textbooks alone would never be able to visualize these concepts as done in the videos
You are very talented and very smart in order to simply such hard concepts to grasp. I think your videos should be shown in classes on the first day of the related class. Thanks once again and keep up the good work!!
Alex Rivera Thanks for that really great compliment. I have received messages from some teachers who say that they are showing my videos in their classes, so this is happening at least in some cases. Thanks.
what many people studying calculus fail to realize is that the integral isn't arbitrarily the area under the curve, but rather is the parametric inverse of the derivate function on the curve itself, and since the derivative is the infinitely instantaneous rate of change of the height and thus the slope of that curve and then the AREA of itself, we can simply say the integral of the derivative is the area of that curve itself. That is, given the derivative is the curve in question.
Would you be Ms. Kira Vincent, the narrator of Mr. Khutoryansky's videos? If so, your excellent voice-over work is every bit as wonderful as the videos themselves, and just as informative!
Awesome video! I was getting very perplexed by the dx X dx square in the final point of the video so thanks for explaining that. Thanks for sharing this.
Nice Visualizations, i always become happy when i see your new video come out :) btw can u a top 5 or top 10 video like "Top 5 mysteries of physics/universe" etc ?
Odin 7 Thanks. I am glad you like my videos. I have seen some of the "top 10 mysteries", etc. type videos, and although they are enjoyable, I don't think that those types of videos are really my style. Thanks for the suggestion, though.
so that's why derivative of y=x^2 is 3 times (x^2 times dx) means the total minimum change (derivative) of this function is the volume of the 3 cuboid which mathematically is 3 times (area of rectangle times small depth dx)
6:40 here is a mistake : the little red square (dX x dX) do not become smaller when the the sides increases. But the ratio between : (little red square surface) divided by (total surface) becomes smaller and smaller numbers between 0 and 1 are a big source of mistakes, in all sciences. Anyway, thanks for your amazing job, visual proofs should be the backbone of moderls scholars
+kjuzehdua ejdnaj, I never said that the square becomes smaller when the sides increase. What I said was that the area of square becomes negligable as dX approaches zero. And thanks for the compliment.
My god... I was knowing the problem was not with me.. It was with the teachers who don't know how to explain.. This is how Mathematics should be taught
ThomasHaberkorn Unfortunately, it now looks like the video about the product rule will have to wait a little bit. I still plan on making a video on that topic, but a few more physics videos are coming first. Thanks.
I am a huge fan of Mr. Khutoryansky's videos, and this one is every bit as excellent as the rest, yet I feel his "final point" is a bit misleading; at approximately 7:15, the narrator implies that the over-looked volume is negligible, since, as she puts it; "Two small numbers multiplied by each other is an even smaller number." Yet, correct me if I'm wrong, but unless I am, this statement applies only when both numbers are less than one. So, for example, if we have an area 1/2 foot by 1/2 foot, the result is indeed smaller, being 1/4 feet squared. However, 1/2 foot is still 6 inches, so in inches, this area would be 6 inches by 6 inches, thus 36 inches squared, which is certainly a larger number than 6! While this may sound like splitting hairs, I would argue that it all depends on one's point of reference, and what one considers "negligible".
This is wonderful! By the way, what is the name of the piece of music that is background for this animation. Is it something by Bach? or maybe Mozart? If so what is the title of the piece. So beautiful.
Thanks for the compliment. The music in this video is from the free TH-cam audio library, and the names of the songs are the following. Far_Behind Allemande
Usama Khan Derivateves are not an estimate. This is due to the fact that as dx approaches zero, the portion of the equation that we are ignoring becomes negligabely small as compared to the rest of the equation. And thanks for the compliment about the video.
why does dx only fill volume on the 3 surfaces but not in the corners? y=x^3 describes the volume of a cube, but if u add volumes on the sides of the cube and not in the corners as you increase dx, its not y= x^3 anymore, is it?
zebleckDAMM I address this at the very end of the video. As dx approaches 0, the volume of the corners is negligibly small as compared to the total increase in volume.
To see subtitles in other languages: Click on the gear symbol under the video, then click on "subtitles." Then select the language (You may need to scroll up and down to see all the languages available).
--To change subtitle appearance: Scroll to the top of the language selection window and click "options." In the options window you can, for example, choose a different font color and background color, and set the "background opacity" to 100% to help make the subtitles more readable.
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No word to say 👌👌👌💐💐 , great job for concept clearing . Can I get more videos on maths and physics plz. If yes plz send me link and how you create this videos
I do not understand how can we visualize the derivative of x
In case you have not already seen them, I also uploaded several other videos in the past several days. As always, for each video that you like, you can help people find it in the TH-cam search engine by clicking the like button and writing a comment. Lots more videos are coming very soon. Thanks.
Eugene Khutoryansky Thank you so much. Best science explanations on youtube. You are a true educator of the mind.
THANK YOUUUUUU I LOVE THEM!!!
Your spatial reasoning skills are amazing. How did you get so good at visualizing mathematics?
Thank you so much.Its very helpful to unsderstand mathematics. :)
Eugene Khutoryansky
As always, this leaves me open-mouthed. Even though I am studying engineering and I find deriving as simple as opening a peanut barehanded (and the simplest derivation is indeed the polynomial derivation), I couldn't imagine being able to actually VISUALIZE a polynomial derivation like this. It left me totally outsmarted. And I am so happy everytime I watch your videos because either I learn something new, or I get something I knew clarified. Only one little thing I'd like to point out: I read somebody having doubts about the effective loss of precision due to the difference between the incremented area and the "lost" area.
Maybe you could have pointed out in a graphical way that the increment is infinitesimal (is it correct? I mean infinitely little) and that dx is actually the smallest increment one could ever imagine. I thought a way to show this could have been making a big zoom on the edge of the cube (or the square) and showing a very little increment over the whole volume/area, so little that not only by saying it, but by even showing it, you demonstrate how little and negligible is the increment dx (and thus the differential dy).
***** Basically every word of that applies to me. One idea I had for visualizing why the missing edges and corners don't affect the result was to show the green squares slowly narrowing until they look like sheets of paper, and have Kira say something like "As the magnitude of dx gets smaller, 3x^2dx becomes a closer and closer approximation of dy"
Adam Thornton
well, actually you are wrong because 3x^2 dx IS dy with no approximation. the notation d(variable) means that we are talking about differentials. If we are approximating a quantity, we should use the limit. In particular, we should be talking of DELTA X and DELTA Y (which are differences and not differentials), whose ratio (DeltaY/DeltaX) is the incremental ratio... whose limit as DELTA X approaches 0 becomes the derivative (in this case 3x^2) with no approximation. Remember that dy and dx are infinitely small numbers, close to 0. And it is their ratio, the ratio of these two infinitely small number, which is the derivative of the function. You can't approximate a derivative, but only an incremental ratio, because the derivative is the infinite approximation of an incremental ratio :)
+Xyneef “The Phoenix” Phaenix is that the specific reason why we don't include dx in coming up with derivatives?
+Terrell McNasty pardon?
derivative of x^2 is 2x(dx) according to the video.. but normally, we only write d/dx[x^2] = 2x
If only i had seen your vids decades ago... Great stuff
Skyturnip
@@richtonge intriguing
Check out 3b1b's channel and search 'essence of calculus'. Your brain might explode
Technically you can't! Since it has been posted only 5 years ago
i genuinely thank you from the bottom on my heart this was sooo good it gave me such an intuitive sense into visualising calculus i have searched books asked all the teacher in my college and outside looked for hours online , but didn't feel satisfied ...but this is so great it doesn't leave me with a new complicated rule , the logic is so clear in your video ,instead of telling us to accept some basic rules you showed it exactly ...and also answered the question the viewer must have about the red area/vol/4d equivalent
THANK YOU SO MUCH i am so glad i found your channel
You can help translate this video by adding subtitles in other languages. To add a translation, click on the following link:
th-cam.com/users/timedtext_video?ref=share&v=tWnvt-8wSeA
You will then be able to add translations for all the subtitles. You will also be able to provide a translation for the title of the video. Please remember to hit the submit button for both the title and for the subtitles, as they are submitted separately.
Details about adding translations is available at
support.google.com/youtube/answer/6054623?hl=en
Thanks.
Your videos on mathematics are always a pleasure to watch thanks to such interesting visualizations! Thank you!
electrocat1 Thanks. I am glad that you like them.
I have never watched such a crystal clear and easy to process conceptualization of the derivative. Wow man.
I am glad you liked my video. Thanks.
wow. atlast, a clear demonstration of what this is about
This a new, interesting, and different way of thinking about derivatives. Thank you.
subscribed! you're a blessing! i always have an itch to visualize mathematical concepts. glad to have found it in your channel! please make more videos :D
+Terrell McNasty, thanks. I am glad to have you as a subscriber. More videos are on their way.
This deserves so many more views. I would have loved to have seen this when I was first learning derivatives. This is so elegant l.
Dan Albl Thanks. I am glad you liked it. I made this video only a few days ago, so hopefully there will still be many more people who will have the opportunity to view this. Thanks.
Once again a great video. You deserve a lot more views and subs!
Falangaz Thanks. Hopefully enough people will share my videos to help make this happen.
Eugene Khutoryansky On almost all your videos you only have a couple of dislikes. That says enough, keep doing what you are doing and after time more and more people will come to appreciate your work.
You, Sir, are a masterful educator! Well done! (As always!)
No one ever fking explained to me why y'(x) can be written dy/dx and ive never thought about it. Thx for this video and keep up the good work!
Every time I have to laugh, and true full joy for seeing how this works and understanding ! It's mind blowing!
I FUCKING ENJOY THESE CALCULUS VISUALIZATIONS OH MY GOd AM SUCH A FAN OF THIS CHANNEL
you are real mathematician,thanks for great video
Once again awesome. :) Those visualisations of mathematical concepts are really refreshing.
Neomadra Thanks. I am glad you liked it.
Never thought I would swear about cal in positive way, these videos are so F'en clear, watching these videos should be mandatory for any class. Textbooks alone would never be able to visualize these concepts as done in the videos
Thanks for the compliment about my videos.
You are very talented and very smart in order to simply such hard concepts to grasp.
I think your videos should be shown in classes on the first day of the related class. Thanks once again and keep up the good work!!
Alex Rivera Thanks for that really great compliment. I have received messages from some teachers who say that they are showing my videos in their classes, so this is happening at least in some cases. Thanks.
Great video, I strongly value the increase in Quantity of videos you share online! keep up the good work!
John Smith Thanks. Lots more videos are coming.
Deep thoughts of physics explained graphically. Inspired me to think physics boldly.
Mind blowing graphics n League apart explanation!!! thnx buddy.. all d best 4 future vids!! hoping to see u soon with loads of them :)
Prasad Beer I am glad you liked it. Thanks. Lots more videos are on their way.
Just brilliant & crystal clear! Thank you sooooo much, my Friend! Positively brilliant!
Thanks. Glad you liked my video.
possibly the best visual proof for derivatives. thank you sir! really good video.
Thanks for the compliment. I am glad you liked my video.
This is amazing! I'm in algebra 2 and you made this so simple that I could understand this! This is incredible!!!
Thanks. I am glad you liked my video.
Great video! It would be amazing you make a video mentions integrals. Anyways thank you again Eugene ur the best!!
Im sorry, i really enjoy your videos, specially calculus ones, keep them coming! good job!
Oliver Lugo Thanks. I am glad that you are that enthusiastic about my videos.
Quality work as usual. Thank you!
TheThePinkPrincess77 Thanks. I am glad you liked it.
Beautiful pictorial representation of derivatives. Newton would approve. And Leibniz.
So well,so good
I'm very happy with explains this
eugene! your videos bring me so much joy!!!!
Thanks. I am glad you like my videos.
So many amazing videos!
*Thank you Eugene!*
Simo Puttonen Thanks. I am glad you like them.
بارك الله فيك يا اخي العزيز
2:28 - Such a good explanation of the power rule. Was watching 3blue1brown and still was having a hard time understanding derivatives.
Glad you liked my explanation. Thanks.
lovely describe.. thanks
Unbelievable. A new video every new day :)
your explanations are amazing but your music choice is even better
Thanks.
what many people studying calculus fail to realize is that the integral isn't arbitrarily the area under the curve, but rather is the parametric inverse of the derivate function on the curve itself, and since the derivative is the infinitely instantaneous rate of change of the height and thus the slope of that curve and then the AREA of itself, we can simply say the integral of the derivative is the area of that curve itself. That is, given the derivative is the curve in question.
for me, you are the best and legend in the youtube mr. khutoryansky. please keep your going. voted up.
noem1977 Thanks for that really great compliment. Lots more videos are coming soon.
Great visualization of the concept!
Kira V Thanks.
Would you be Ms. Kira Vincent, the narrator of Mr. Khutoryansky's videos? If so, your excellent voice-over work is every bit as wonderful as the videos themselves, and just as informative!
Oh Gash, incredible animation.
your videos are amazing. you make things simple. thank you very much.
Thanks for the compliment about my videos.
Awesome video! I was getting very perplexed by the dx X dx square in the final point of the video so thanks for explaining that. Thanks for sharing this.
Thanks.
Great video, as always!
MadHat Production Thanks. I am glad you liked it.
awesome video cant thank you enough
once again awesome video
Thanks. I am glad you liked my video.
thanks! beautifully done!
Roni Salnac Thanks. Glad you liked it.
i really love your voice.
Totally mindblown
attractive way for illustration, thanks a lot
raed sheyyab Thanks. I am glad you liked it.
Great video Eugene, keep it up!
RapiBurrito Thanks. I am glad that you liked it. Lots more videos are on their way.
great animation bhaiya. thanku for your efforts
Thanks.
Videos are incredible, as always. Pls do more basic and higher level calculus!
Thanks for the compliment. More videos on all topics are on their way.
Another great video!
Theenerd ジェームズ Thanks. I am glad you liked it.
This is excellent, thank you.
Mark G I am glad you liked it. Thanks.
Great video thank you so much!
+anda77711, glad you liked it. Thanks.
This great video is should be shown to all math teachers in schools around the world. Then teach to students.
Thanks for the compliment about my video.
Thanks for the video!
***** Glad you liked it.
Great explanation!!
Glad you liked my explanation. Thanks.
One thing I don't understand how this channel is not followed by millions ?
Thanks for the compliment. Maybe in a few years, it will be.
Nice Visualizations, i always become happy when i see your new video come out :) btw can u a top 5 or top 10 video like "Top 5 mysteries of physics/universe" etc ?
Odin 7 Thanks. I am glad you like my videos. I have seen some of the "top 10 mysteries", etc. type videos, and although they are enjoyable, I don't think that those types of videos are really my style. Thanks for the suggestion, though.
Eugene Khutoryansky no problem keep it up!!!
I love how these things can be broken down intuitively
分かりやすスギィ
this is the real essence of calculas
Thanks for doing this!
Glad you liked my video. Thanks.
haha that’s cute (: nice to see it animated
you're awesome gays....
thanks a lot...
bwv 813
Putsmeiser Thanks. I am glad you liked the video.
MY ENGINEERING WOULD HAVE BEEN MUCH EASIER IF I HAD THIS AND AFTER SEEING THIS MY ENGINEERING IS BECOMING MORE INTERESTING
This video is like explaining
Derivatives with integral stripped approach (graphs)
so that's why derivative of y=x^2 is 3 times (x^2 times dx)
means the total minimum change (derivative) of this function is the volume of the 3 cuboid which mathematically is 3 times (area of rectangle times small depth dx)
please prepare one video on finite element analysis.....for better visualisation.....how those software works
THANKS EUGENE
Excellent.
Thanks.
You are doing god's work, i said it a couple weeks ago i'll say it again
Thanks for the compliment.
6:40 here is a mistake : the little red square (dX x dX) do not become smaller when the the sides increases. But the ratio between : (little red square surface) divided by (total surface) becomes smaller and smaller
numbers between 0 and 1 are a big source of mistakes, in all sciences.
Anyway, thanks for your amazing job, visual proofs should be the backbone of moderls scholars
+kjuzehdua ejdnaj, I never said that the square becomes smaller when the sides increase. What I said was that the area of square becomes negligable as dX approaches zero. And thanks for the compliment.
thank you so much
You are welcome and thanks.
Wow!
ashish nigam Glad you liked it.
excellent 👍
Thanks. Glad you liked my video.
Is there one explaining W the derivatives of trig functions?
could you please make video on metric spaces ?
👍👍👍🌹🌹🌹
My god... I was knowing the problem was not with me.. It was with the teachers who don't know how to explain.. This is how Mathematics should be taught
Thanks.
My mind just blew out
:)
Adam sanki tadil-i erkan ile namaz kılıyormuş gibi anlatıyor, helal olsun. Your explanation looks like praying well, thank you soooo muuuuch.
Thank you✨✨✨
You are welcome and thanks.
Brilliant
Thanks.
Thank youuu
You're welcome and thanks.
very cool. never have thought about it this way. you should do one about the product rule.
ThomasHaberkorn That's the next video.
:)
ThomasHaberkorn Unfortunately, it now looks like the video about the product rule will have to wait a little bit. I still plan on making a video on that topic, but a few more physics videos are coming first. Thanks.
I'm happy with the videos that you have made already, if you make more, kudos to you!
I just completed and uploaded the video on the product rule.
Question ... why do we ignore the dx*dx square remaining when extending a square by dx in two dimensions?
Because as dx approaches zero, the quantity (dx*dx) becomes negligible compared to the other quantities.
wooow
i would've love to see what x^4 dx would look like visually. Amazing video though.
+Misael Cifuentes, I show four dimensional cubes in some of my other videos, and thanks for the compliment.
Please mughe btado kis platform. Ya kis app ,software pe bna sakte h?
great , excellent
Thanks. Glad you liked my video.
@@EugeneKhutoryansky
on your channel videos on physics are amazing.Hopfully i'm going to watch all of them.
@@EugeneKhutoryansky
How long have you created this channel?
I uploaded my first video 9 years ago. Thanks.
I am a huge fan of Mr. Khutoryansky's videos, and this one is every bit as excellent as the rest, yet I feel his "final point" is a bit misleading; at approximately 7:15, the narrator implies that the over-looked volume is negligible, since, as she puts it; "Two small numbers multiplied by each other is an even smaller number." Yet, correct me if I'm wrong, but unless I am, this statement applies only when both numbers are less than one. So, for example, if we have an area 1/2 foot by 1/2 foot, the result is indeed smaller, being 1/4 feet squared. However, 1/2 foot is still 6 inches, so in inches, this area would be 6 inches by 6 inches, thus 36 inches squared, which is certainly a larger number than 6! While this may sound like splitting hairs, I would argue that it all depends on one's point of reference, and what one considers "negligible".
This is wonderful! By the way, what is the name of the piece of music that is background for this animation. Is it something by Bach? or maybe Mozart? If so what is the title of the piece. So beautiful.
Thanks for the compliment. The music in this video is from the free TH-cam audio library, and the names of the songs are the following.
Far_Behind
Allemande
@@EugeneKhutoryansky Thanks. The first piece sounds like Mozart. The second, like Bach.
sir can u share the link of derivative of sinx and cosx
Great work.
What are you using for creating these videos?
+Nadiia Chepurko, Thanks for the compliment. I make the 3D graphics with "Poser." Thanks.
So when we do derivatives to work out gradients is it actually an estimate of the gradient? Great videos by the way.
Usama Khan Derivateves are not an estimate. This is due to the fact that as dx approaches zero, the portion of the equation that we are ignoring becomes negligabely small as compared to the rest of the equation. And thanks for the compliment about the video.
why does dx only fill volume on the 3 surfaces but not in the corners? y=x^3 describes the volume of a cube, but if u add volumes on the sides of the cube and not in the corners as you increase dx, its not y= x^3 anymore, is it?
zebleckDAMM I address this at the very end of the video. As dx approaches 0, the volume of the corners is negligibly small as compared to the total increase in volume.