The Multi-Variable Chain Rule: Derivatives of Compositions

[@lolololol632]

You literally saved me hours of work because your explanation is so intuitive and straightforward, and in such a small amount of time. I wish you the best in future.

[@DrTrefor]

So glad it helped!

[@balakrishnakumar1588]

Why he isn't famous yet ? Great explanation sir.

[@subhadeeppal917]

Really I just love your videos. 🤩

[@NuclearPhysix]

He is famous. You may need to remember that not many people like or do mathematics, at least on KZbin, you will not expect his followers to be the same number as some funny cat videos posts viewed by anybody else. He hi up there with MIT Herb Gross in my opinion

[@AbhishekKumar-jg7gq]

Because he has a difficult accent which non native speaker can't understand

[@aashsyed1277]

@@AbhishekKumar-jg7gq no.

[@tevinabeysekera6038]

@@AbhishekKumar-jg7gq ?

[@garrettgeffre1792]

If you’re only here to see how it works look at 10:12. Great video man thank you.

[@Lostwolf16]

Content and quality of video is masterclass, hope to see a rise in quantity of other concepts as well. Thank you

[@hu900]

I'm so happy that I found this, he explains it realy well. At 3.20 "If you only change w" should be "If you only change x". No problem though, it is clear anyway. Thank you so much for this video!

[@vaisuliafu3342]

these videos are so good... i hope you are dreaming big enough with your channel. This is the future of math education

[@mimstudent8662]

I am from Bangladesh.U teaching method is very good.I can get easily understand.I saw many videos but u videos really well done.Thank u so much.Sir

[@honkhonk8009]

Love the video bro. Im a CS major and was struggling to figure out how chain rule worked for backrpopagation. The chain rule seemed easy enough on textbooks but i never understood what the dependency chart thing was, or how it would be extended to other examples This just explained it perfectly

[@daumel98]

I love you. Visualizing a dependency graph makes this so easy! I finally understand backpropagation in neural networks

[@EfremTesfaye-cz7tl]

I get this video after a period of time but i regret about the time before. really i appreciate you continue don,t stop here .

[@belemaayonoadu9219]

Brilliant! I can't believe how you made this concept extremely easy!

[@farhansadik5423]

absolutely brilliant explanation. massive respect to you sir!

[@joyghosh3858]

This is how math should be taught.. Just superb.

[@DrTrefor]

Thank you!!

[@muhammedalam1203]

one of the best explanations out here. Thanks Sir.

[@amansingh-ww2qc]

Best maths teacher ever

[@xiu8548]

you r not only more handsome than my professor, but also give GREAT explaination! ! My professor gave lectures in 2 hours, you explain it in few mins.

[@immortalkarin]

Great videos man, you really have a very charismatic way of explaining math.

[@isakwatz11]

Impressively simple yet effective expanation!

[@sharminahmed4324]

best explanation that i came across

[@aravindhvijayanandan3010]

Great exposition of a difficult concept, Dr. Bazett Subs from India

[@jankowalski8102]

Great content! Greetings from Poland!

[@gokulakrishnansaravanan7475]

u are really doing great sir. giving the real insight to mathematics .

[@Chris-ng9zi]

You are an excellent teacher!!! Keep up the good work.

[@sahilafroj277]

Beautifully explained sir. Love you.❤️

[@sandunmunasinghe9469]

you are the best and i really like your videos

[@koprofessional7280]

Thanks sir really your explaination is very good

[@jitendermeena9480]

I loved the tree diagram. Great job sir 👍🏻

[@billycheung5114]

Your video help me a lots !❤

[@akshitk6818]

Really Awesome series of Calculus 3 and 4! Covers all the aspects that are usually taught in year 2! Your explanations are way better than my professor! Your videos have truly helping me in understanding better!

[@DrTrefor]

Glad you like them!

[@PD-vt9fe]

Great video as always. It helps me a lot to rebuild my math background. Keep it up!

[@crimfan]

A very nice explanation of the total derivative.

[@yoavmor9002]

Index notation and Einstein convention make this very easy to remember. But I don't think most folks are ready to display all variables as x⁰, x¹, x², x³, etc...

[@ossahmadrezaazimikohnabi5108]

This wss the highlight of my day. 🎉❤😭😍

[@yosafendrafendra7960]

Hello Dr Trefor please make a playlist about Partial Derivatives Equation, i think a lot of people will need it. thanks a lot

[@DrTrefor]

I plan to!

[@ahmedmohamedkhogle6100]

Nice keep going we need such those videos 🙂

[@discoveryofphysics9303]

Thank you Sir. It helped a lot.

[@hakaneskici2771]

Thank you for the explanation sir

[@continnum_radhe-radhe]

Thank you sir 🔥🔥🔥

[@sestro4233]

Nothing to say but thank you.

[@vct98890]

OMGG THANK YOU SO MUCH SIRR

[@HasanRaza-pe2sy]

Great content. In india many of us study this in grade 11 and 12. As how i know as i am in 12 currently

[@arpityadav.832]

burh it is of multivariable its teaches in college 1st . from which board r u?

[@billhopkins8330]

Great explanation!!

[@frommarkham424]

it's useful in machine learning

[@realchatlabs]

Do I understand it right that the multi-variable chain rule the same as the single-variable chain rule (f . g)'(t) = f'(g(t))g'(t) with the difference only that you have a dot product between f'(g(x)) and g'(x) instead of a regular multiplication? (assuming that g(t) = [x(t), y(t), ...] to fit your examples).

[@salvatoregiordano9050]

Excellent video and explanation sir! I really appreciate this. Do you have any idea where I can find a video that proves the formula for the chain rule you described? Thank you so much!

[@bilalabbad7954]

Thanks

[@Avinash_Avee]

Tnqsm 🙏

[@doxo9597]

I still don’t understand why it’s the sum of the two?

[@edwardhsieh7144]

Think of the components as vectors, then it is just the addition of two vectors.

[@omer7895]

What would be the gradient of w?

[@ugursoydan8187]

why we added the change due to y to change due to x? is there a proof of that?

[@abdullahmohamed2083]

Thank you thank you sooo informative

[@suvanshmahajan5902]

Can anyone tell me if this is calculus of two independent variable(x,y) and here both these variables are dependent on t, so basically both are not independent of each other.How???

[@DrTrefor]

Yes in this situation we still call x and y independent even if they are both functions of the same variable.

[@felixgomez5085]

I have to tell you sir. You design usefull videos, with nice visuals. But you need to upgrade your sound device... It's mandatory at this level !!!!!!

[@DrTrefor]

i actually since have!

[@giuseppecammarata7528]

Thank you! Would it have been an error if I had written the symbol of the partial derivative in lieu of dx/dt and dy/dt (second row in final conclusion)?

[@joaomattos9271]

Amazing!!

[@ronycb7168]

Thanks ... Also the chain rule looks a lot like the total differential divided upon dt

[@khushinegi1363]

What about the higher order derivatives in two variables?

[@khushinegi1363]

How will we calculate them?

[@DrTrefor]

Well we mostly do what we just did, but twice. So if you can do, say, the partial with respect to x then just do that again to get the second partial with respect to x.

[@sharifullahdanish4480]

As you said we can directly solve it via putting the values of the x & y, so if you would do it, we will appreciate it. thanks..

[@mathadventuress]

hi dr trefor, can you please make a video or have you already on 2nd derivatives? say if z=f(x,y) and x=x(r,s) and y=y(r,s)...and we want to find the 2nd derivative of z with respect to x or y...i have an example in my book and i just dont understand it. i follow along the first derivative just fine. but then it says d/dr times the first derivative...which so far makes sense, but then it looks like it is doing implicit differentiation or something? please, thanks!

[@edwarddi3833]

nice video, very informative! Thanks! however, what about the second derivative of f(x(t), y(t))?

[@fullfungo]

Just take the derivative twice

[@三點一四一五九二六]

Still don't understand, why can't I just use dw/dt instead of partial

[@ojkwame]

I think you can , eg. At 9:56 , if you substitute the function of x with the variable x and like wise y

[@Nik-qh7cq]

What if we have f(x,y) and a g(x,y) = (n(x), m(y)) and we need the derivative in respect of x for f(g(x,y))

[@keerthanadiga3781]

why single independent variable chain rule has product of 2 slopes why they had to multiply the 2 slopes?? can anyone answer .... it would be a chance for others to think

[@enzoys]

I mean, it looks like you can just substitute the t expressions in both x and y and have a normal chain rule

[@nadernaysak]

You're a great teacher really, but your voice isn't clear and it sounds like a little noise there. Try a better mic. I WISH YOU THE BEST!

[@josephhajj1570]

Mr what's the proof of this chain rule😘😘😘

[@aditube8781]

AMAZING

[@slowsatsuma3214]

I love you

[@abnereliberganzahernandez6337]

I joined

[@DrTrefor]

Hey thank you so much! Glad to have you:)

[@Darkmatterkun]

why does the theorem still hold true when the cross example proves it wrong

[@altuber99_athlete]

Great explanation! The pauses were on time, but maybe talking a bit slower can help the viewer to grasp the concept under discussion. Regardless, nice job! One question. In your example, we had "w = f(x,y)" (and particularly "w = x^2 y"), where at the same time "x = g(t)" (and particularly "x = 2 t + 1") and "y = h(t)" (and particularly "y = t^3"). That's fine, but I have a slightly different example. Suppose we have a function "w = f(x,y)" (without knowing any particular expression for "w"), where at the same time *"x = g(u,y,t)"* (not any specific expression for "x") and "y = h(t)" (not any specific expression for "y"). *Would the derivative "dw/dt" still be given by "∂w/∂x · dx/dt + ∂w/∂y · dt/dt, or would the formula change?* Notice the main difference between your example and mine is that in yours, "x = g(t)", while in my example, x = g(u,y,t)" where "u = i(t)".

[@dinigi]

Honestly, I don't really care about how and why this works on a fundamental basis. I am just looking to apply it correctly..

[@huijiang3051]

Good than common teacher ,bu also not clear and to some degree, is a waste of time and energy to watch

[@easymathe4all6247]

kzbin.info/www/bejne/ZoHTlGp3r6-nrKs full concept of chain rule

[@birdhanhansdah8580]

hhhha