Khan Academy Video 1 (Gradient vs. Directional Derivative)

[@ehinspections]

This video has to be the best explanation of the Gradient in KZbin, well done!

[@rhondahughes9648]

Thank you so much!

[@joereadman4390]

can we all just take a moment to appreciate that she managed to write the word 'gradient' whilst spelling the word 'tail' out loud? this is a talent!

[@مريَم-ط5م7غ]

meanwhile, me who can't even spell her own name while spelling her father's name out loud

[@nuklearboysymbiote]

tale* she literally spelled it out loud too

[@wwmheat]

Wow, it's a standing ovation!! Having watched all the great content available now in 2022 on this topic (3b1b, Grant's explanation in Khan academy and others), I still couldn't get why directional derivative can be expressed by gradient and dot product.. I mean, it certainly makes sense as a vague statement, it has an intuitive support, but I couldn't get it rigorously, including how it can be derived purely in terms of definition of derivative. And now finally it's crystal-clear!

[@rhondahughes9648]

Thank you for those kind words!

[@scottkelly3062]

I see you just made this video a few months ago. I hope you make some more videos. This was the best youtube video on any topic on Calculus I have watched. I find that most videos rush into an example or start off a concept slow and when it gets to the abstract part speed it up. This one stays consistent throughout and maybe even slows down to help the viewer. This was just great.

[@rhondahughes9648]

+Scott Kelly Thank you, I appreciate that!

[@muralidhar40]

I was hopping from one video after the other on youtube to find the difference between DD and Gradient, My journey has come to an end. Thank you madam/miss.

[@rhondahughes9648]

I'm happy to hear that!

[@ozzyfromspace]

2:57 When she said "at any rate..." I immediately thought of professor Herbert Gross (an extraordinary MIT math educator from the 1960's). I like Rhonda's style and pace of teaching, it's almost like a conversation. Best wishes!

[@rhondahughes9648]

Thank you!

[@EvaPev]

Wow! I'm impressed! Great intuitive explanation! Thank you very much for your effort!

[@rhondahughes9648]

Thank you, Evelina.

[@mateennaser5347]

Please Miss Rhonda could you help me?I need your help, please if I could contact with your e-mail. My e-mail is ([e-mail]). Thanks.

[@LearnPhysics-xz3mf]

I just can't think you enough ma'am, it's amazing, the relationship between directional derivative and gradient is just amazing, I'm just overwhelmed by the beauty of mathematics and teaching 💕💕💕

[@rhondahughes9648]

Thank you so much!

[@yj6439]

Thank you very much for your video, Rhonda! It’s been a very long time ever since I first studied it, and I can tell you this. Despite all fashionable, computational stuff of our days, there’s nothing like the old school way to learn calculus! You covered the whole package in 14 minutes. Thank you again!

[@rhondahughes9648]

You are welcome!

[@robjows]

Amzing Video. In my Calculus 1 class we've jumped from Integration techniques to the gradient vector and multi-variable chain rule - simply being taught the equations with no background on what we're actually doing. This video answered the majority of my questions.

[@dangargiullo9634]

Not even halfway through the video and I already feel like it all makes sense. By far the most helpful video I've watched on any multivar topic. Thank you SO MUCH!!!!

[@rhondahughes9648]

Thank you!!

[@jacobvandijk6525]

In short, the well-known partial derivate (in some point P) is just a special case of the directional derivate, using the standard-basisvectors as unit-vectors.

[@rhondahughes9648]

Precisely!

[@lythien390]

Wowww!! It's so fascinating. Thank you for being my savior in Calculus!

[@rhondahughes9648]

Thank you!

[@depresso18163]

This is amazing. I wish this channel had more videos on multivariable calculus.

[@rhondahughes9648]

Thank you!! I've been working on other videos, but will try.

[@alexramirez5104]

Haha! The "Is that middle earth? I don't know" remark had me cracking up! Thanks so much!

[@rhondahughes9648]

Thank YOU, Alex!

[@Raynover]

Enlightening from start till end. Unbelievable! Great graph too.

[@rhondahughes9648]

Thank you so much for your kind words!

[@justwatchingmathvideos130]

thanks, now i see that the vector can be used in a parmetric equation. that helped a lot.

[@student6830]

I solved an entire problem set of directional derivatives but didn't really know what they were about. This video helped me understand. Thank you.

[@johnholme783]

Beautiful! So simple, yet so useful.

[@S.Sagarjsr]

Make some more videos mam they are helpful for us to understand the concept only 2 video😓

[@rhondahughes9648]

I'm working on it! Thank you.

[@salehahmed4139]

Best explanation of directional derivative, now I actually understand what the directional derivative" means.Thank you

[@rhondahughes9648]

Thank you!

[@yavuzanyavuz]

clearly one of the best video( maybe the best) about these topic. Appreciated!

[@rhondahughes9648]

Thank you very much!

[@marshallking6478]

Thanks so much for your teaching, it really helps me a lot! Salute! And hope for your future classes in KZbin~

[@rhondahughes9648]

Thank you so much!

[@johnholme783]

Such an simple equation, yet so useful! Excellent derivation, thank you!

[@rhondahughes9648]

Thank you!

[@johnholme783]

@@rhondahughes9648 Your welcome! Hi Rhonda; I’m currently studying physics at degree level and I was wondering if you could recommend a maths textbook, preferably an illustrated one for physics at this level. Regards John.

[@isaiahvalencia5954]

Ms. Hughes! fantastic video! you give concise, intuitive, and rigorous explanations! we'd all like to see more from you! thank you!

[@rhondahughes9648]

Thank you very much, Isaiah!

[@hesokaheso855]

Man i Spent hours on youtube, trying to understand this, Finaly i can see where this was coming from, thank you very very much.

[@rhondahughes9648]

Thank you, Hesoka!

[@salehahmed4139]

Best explanation of directional derivative. Thank you. Please post more videos on multi variable calculus.

[@rhondahughes9648]

Thank you!

[@epilepsyawareness]

very well done. concise. thanks.

[@viktoriaosadchuk1601]

Great video!But I have question towards 11:24 ,you said,that when t=0,isn‘t when t is approaching to 0,but not equal to it?😊

[@rhondahughes9648]

Thank you. The derivative is at t=0 (but the derivative is defined using a limit as t approaches 0).

[@viktoriaosadchuk1601]

@@rhondahughes9648thank you!

[@rashmisingh6361]

Mam please upload some more videos on calculus. Finally I understood their geometrical meaning.. Mam thanks a lot, you are doing a great work!!

[@rhondahughes9648]

+Rashmi singh Thank you!

[@RepeatingData69]

Great approach to deriving it!!! I hadn’t seen it done this way. Very easy to remember.

[@rhondahughes9648]

Thank you very much!

[@CDinkle]

Very helpful, and the drawing explaining the two partial derivatives was also very clear. Thank you.

[@rhondahughes9648]

You're very welcome.

[@dr.rajnandkeolyar4482]

Excellent video...Very helful

[@rhondahughes9648]

+Dr. Raj Nandkeolyar Thank you!

[@santoshijyothi7661]

Awesome.... impressive..... to the point.....I can't even imagine to find so much explanation anywhere

[@rhondahughes9648]

Thank you!

[@mkalysto]

Briliant! Clear and informative! Thank you

[@rhondahughes9648]

Thank you!

[@gloryths]

One of the best explanations out there. Thanks

[@rhondahughes9648]

Thank you so much!

[@xavier.antony]

Wonderful explanation just using marker and board.. Teaching Mathematics is an unique talent, not everyone can do that. Thank you..

[@rhondahughes9648]

Thank you so much!

[@mpgrewal00]

well done.. you explained a complex concept in a very easy to understand fashion. Your presentation style is impeccable.

[@rhondahughes9648]

+mpgrewal00 Thank you so much for your kind words!

[@Justmetmt24]

Who doesn't like stories?! Very well put. I now see how everything is linked together. Especially the gradient for vectors in physics =0

[@rhondahughes9648]

+Justmetmt24 Thank you very much!

[@111abdurrahman]

absolutely fantastic..... you should make more videos... you can use ur own channel as platform.

[@rhondahughes9648]

Thank you so much!

[@jessewilliams1276]

This was much better than the video that they had on Khan Academy. At first i was upset that she named it the way she did, but after watching, i was glad that i was “click-baited” into watching this video 😅

[@rhondahughes9648]

Not "click bait." This was an entry to the Khan Academy Talent Search several years ago.

[@haroonj4298]

They way you expressed the concept is the way we wanted, it is the way which fulfill our thirst and remove headache, diabetes and pregnancy.

[@rhondahughes9648]

Thank you! That is quite a compliment.

[@adnansakeeb739]

OMG you are so good at what you do ! it instantly made sense. TYYY.

[@rhondahughes9648]

Thank you SO much!

[@richardli745]

This is yet the best video I've seen on KZbin explaining Directional and Gradient derivatives. Please make more future posts.

[@rhondahughes9648]

+Richard Li Thank you! Working on it:)

[@yusong1141]

Beautifully proven, took my breath away!

[@rhondahughes9648]

Thank you so much!

[@SamirKhan-os2pr]

This was very useful. My understanding on calculating the Jacobian matrix over multidimensional planes has improved ;)

[@rhondahughes9648]

Thanks so much!

[@doxo9597]

When someone asks me “why?” I always respond with “y_0”.

[@garrettnicolay6310]

This was amazing. Eyes officially opened

[@rhondahughes9648]

Thank you!

[@jahansaid6382]

You opened my mind, now I can understand very profound this topic!! Thank you Rhonda :)

[@rhondahughes9648]

Thank you for your kind words, Jahan!

[@rhondahughes9648]

Thank you so much, Jahan! I appreciate your comment.

[@yadpreetcheema4806]

by far the best video I've found on this topic.

[@rhondahughes9648]

Thank you so much!

[@chainesanbuenaventura2874]

I'm amazed! Thank you!

[@rhondahughes9648]

You're welcome:)

[@CR_07770]

@@rhondahughes9648 why you stop making videos.

[@abylkaiyromar4149]

very informative lesson, thanks

[@CardiganBear]

Thanks for this very nice explanation of the directional derivative. I really like the way you start with this concept and then (in the following video) move on to show that the directional derivative has a maximum value when it is parallel to the gradient.

[@rhondahughes9648]

Thank you, CardiganBear!

[@whitewalker608]

I absolutely don't know why you have the like bar off. This is literally the best explanation on youtube for this. I have watched original khan academy videos for this. They didn't show the mathematical proof for directional derivatives through chain rule. I legit googled and read on stackexchange why the directional derivative is the dot product product of the gradient and the vector. Plus rest of the stuff you explained very intuitively. While watching Khan Academy I had to visualize r + hv on my own with a little bit of google search.

[@rhondahughes9648]

Thank you very much. I appreciate your kind remarks!

[@nichkvn]

You did a wonderful job! Great clarity!

[@rhondahughes9648]

+Nicholas Van Nest Thanks so much!

[@PhilV205]

I hope to see many more videos from you. I had a hard time seeing the difference between the two but those days are long gone. Thanks again

[@Jax-ke6jf]

I was so confused on this until this video, thank you so much!

[@rhondahughes9648]

Thank you!

[@pratyayadeepsahoo3703]

this concept was explained in a complicated way in clacalus book but ur practical explanation cleared that complicated explanation thank u soooooooooo muchhh

[@rhondahughes9648]

Thank you! Glad it helped.

[@DavetheBrave420]

5:12 "Why = Why not?" Sounds about right

[@rhondahughes9648]

+Dave the Brave :)

[@TeotoniodeCarvalho]

Very kind of you to share that! Thanks a lot!

[@rhondahughes9648]

You're welcome!

[@akhileshroopan7793]

actually we need two kinds of tutors, the one who teaches us tricks and hacks for solving problems and the other who explains the shit out of it to make it absolutely clear. you madam is the latter one😂👍..

[@rhondahughes9648]

Those are kind words. Thank you very much!

[@mimipakret]

Such a brilliant explanation .. but no more videos ?

[@rhondahughes9648]

+mimipakret Stay tuned!

[@leeszefoo9492]

Wow, such a clean and interesting presentation of the topic. Helped me clear a lot of confusion. Thank you so much!

[@rhondahughes9648]

+Lee Sze Foo Merci!

[@khangvu8759]

Best explanation of the subject.!

[@rhondahughes9648]

Thank you so much!

[@rhondahughes9648]

Thanks very much!

[@benjaminhobson2085]

You are better than my professor. Thanks!

[@Japzastronomy]

Thank you so much, Rhonda! Finally a wonderful explanation to the concept. Good job! :)

[@rhondahughes9648]

+Japjee Kaur Thank YOU, Japjee! I appreciate that.

[@תומרגדליהו-ה1צ]

The best explanation I found on the net

[@rhondahughes9648]

Thank you so much!

[@rajarshichatterjee3281]

this somewhat also gives an intuition about directional derivatives being generalisation of partial derivatives .

[@venu_rao_1]

Geometrical interpretation superb,

[@rhondahughes9648]

Thank you!

[@venu_rao_1]

@@rhondahughes9648 , one small doubt , when gradient F dotted with unit vector what will happen to gradient F? gradientF is a vector function right, that logic till now i didn't get.

[@abdelstar3999]

thank you very much

[@rhondahughes9648]

You're welcome!

[@shockban6725]

Incredible explanation!

[@rhondahughes9648]

Thank you so much!

[@powertube5671]

This was excellent. Why can I not find this in the Khan academy play list. This is very clear. The explanation I found in Khan Academy is more confusing.. Thanks so much for posting this.

[@rhondahughes9648]

I submitted this for the Khan Academy Talent Search several years ago, hence the KA hashtag. I also worked for them as a content creator, but this is not an official KA video. Thank you!

[@powertube5671]

@@rhondahughes9648 Thanks for your reply. I am actually reviewing Maxwell's equations and needed a refresher on these concepts. Fortunately, I learned in college to use many sources or explanations, especially if one instructor or book was harder to understand. I found your video by searching after I had taken the entire playlist on Khan Academy on this subject.

[@TaahirBhaiyat]

Hi Ronda. I really appreciate this video, as my engineering maths lecturer admitted that she could not explain the concept of directional derivatives, however, she did just show us the method of computing it. I now properly understand what's going on, and once again, I'm loving calculus! Thank you so much.

[@rhondahughes9648]

+Taahir Bhaiyat Thank you so much, Taahir! Good luck with the rest of your math!

[@TanEbear]

This is really good and so clearly presented! Wish there were more videos.

[@rhondahughes9648]

Thank you!

[@kormosmate2]

Maybe i missed something, but at 12:30, in df/dt, why did we added the the two paritals together? Where does that come from?

[@MichaelZibulevsky]

Simple and intuitive explanation. Thanks!

[@rhondahughes9648]

You are welcome!

[@vikassoni1760]

Awesome maam

[@rhondahughes9648]

Thank you so much!

[@siddharthtyagi9133]

Thanks for this video. Was finding bit difficulty in this topic but this video gave gave me that Epiphany and then I was satisfied ❤️❤️😭😭😭thank you

[@rhondahughes9648]

Thank you so much!

[@andeslam7370]

Nice video, somehow I could get my intuition only after watching this video. thanks a lot rhonda

[@rhondahughes9648]

You're very welcome!

[@thinkanddo2352]

Thank you so much Ms Rhonda!That was extremely helpful!

[@rhondahughes9648]

You are very welcome.

[@safaali1330]

The best video I have seen What a beauty

[@rhondahughes9648]

Thank you very much!!

[@johnbatchler8551]

Great job

[@lordrothschild4627]

Loved the middle earth reference.

[@rhondahughes9648]

Thank you!

[@9888565407]

Thanks Rhonda, you are a life saver

[@rhondahughes9648]

You are very welcome.

[@gurleenkaur9601]

Great explanation ma'am. I wish my economics teacher taught as wonderfully as you do. Lots of admiration!!!

[@rhondahughes9648]

Thank you very much!

[@fariazislam4077]

Finally found a tutorial which rocks

[@rhondahughes9648]

Thank you so much!

[@dioutoroo]

Thank you! Very nice explanation!

[@rhondahughes9648]

Thank you!

[@bubbleteamath5352]

Your videos are awesome! Appreciate them a lot :) Sad I didn't find it earlier, cause that could've help in my multvar class. Would you mind a question? I has taken this class just a couple of months ago, however, now when I am in my PDE class, I realized a lot of what I was hoping is in my head solidly, is actually not XD. How do you "keep it" for years?

[@rhondahughes9648]

Thanks you! I was the same way. But after many years, I can't seem to get it out of my head. It's just there, comfortable and a source of pleasure.

[@guiray2000]

Very good explanation.

[@rhondahughes9648]

Thank you!

[@GradStudentTutorials]

You made a fantastic video! I've been trying to break my old habits of only memorizing formulas and brain dumping on exams. So I'm seeking out videos that 1.) pique my interest in the subject 2.) explain what the concepts actually mean Your video hit both of these marks. Most other videos merely show you the "steps" and how to compute which can easily be found in a boring textbook. But we all know that memorizing steps can get you into trouble on exams sometimes. Also, Your introduction makes Gradient vs. D.D. sound very interesting. Well anyways thank you for your content. I will be watching your other videos now! :)

[@rhondahughes9648]

Thank you for your very thoughtful feedback. I really am glad my effort worked for you.

[@SoumilSahu]

This video is amazing,but could you make another one explaining where the formula for the multivariable chain rule came from?

[@solomonv4184]

Awesome explanation!

[@aaryanbudhirajamusic6874]

This was extremely helpful

[@rhondahughes9648]

Thank you!

[@S.Sagarjsr]

waooo so nice...explanation You explain things graphically which is not done in our class they only use formula

[@rhondahughes9648]

Thank you very much!

[@S.Sagarjsr]

mam you make some more video on stoke theoram

[@rhondahughes9648]

I've been thinking about that!

[@ankurbharti997]

It was little bit tough to understand at first but it's amazing... Whole concept is crystal clear now ... THANK YOU SO MUCH...🙂

[@rhondahughes9648]

Excellent!

[@Jalpow]

Great video, very helpful!

[@rhondahughes9648]

+Aaron Cheong Thank you!

[@VikasSharma-tv4hn]

Thank you Rhonda! This will help me in understanding the concept much better 😊.

[@rhondahughes9648]

+Vikas Sharma You're welcome, Vikas.

[@avi-brown]

Excellent video, thanks so much! As an Israeli i am curious what is Hebraic about the "x naught, y naught" notation.

[@rhondahughes9648]

Thank you! I misspoke. I wasn't referring to the naughts, but rather the symbol for gradient. I have been corrected!

[@avi-brown]

@@rhondahughes9648 Huh, that's really interesting! I looked into it and you're totally right- apparently the Greek "nabla" comes from the Hebrew word "nevel" (נבל) which is a generic word for harp or lyre. Very cool!

[@avi-brown]

@@rhondahughes9648 I see that now^ you said "symbol", not "notation" so I should have understood ;P. Thanks again for the video!

[@rhondahughes9648]

​@@avi-brown Thanks! So I'm not crazy. I was sure I had read it somewhere. Now if I am corrected again, I will respond with confidence.

[@abhishekkandwal5753]

There is hope...I realised after watching this video

[@rhondahughes9648]

Thank you! There is always hope, even in these times.

[@josegadelha8271]

Beautiful!!

[@rhondahughes9648]

Thank you so much!