This is the simplest case of taking the derivative of a composition involving multivariable functions.
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@acruzp8 жыл бұрын
YES! 3blue 1 brown! Khan Academy really is getting the best of the best.
@johnkent89725 жыл бұрын
I literally gasped when I recognized your voice! Sort of like seeing a celebrity in your hometown. Sir you are awesome.
@luisalejandrorudyorozcomor74206 жыл бұрын
3Blue1Brown????
@lopkobor69164 жыл бұрын
y e s
@harry_page3 жыл бұрын
Multivariable Calculus Episode XXX: Return of the Grant Also, a chain rule intuition prediction: think of the parametric functions x(t) and y(t) instead as a vector valued function r(t) = x(t)i + y(t)j, so from the previous few videos, we know that a tiny nudge dt along the curve can be represented by the vector derivative r'(t) = x'(t)i + y'(t)j (which is tangential to the curve). Then think of f(x(t), y(t)) as projecting the curve onto some surface in 3d, so the total derivative df/dt can be thought of as a directional derivative: nabla of f dot dr/dt which is ∂f/∂x*dx/dt + ∂f/∂y*dy/dt
@chiquita_dave5 жыл бұрын
Thank you SO MUCH for this video! I am learning the Slutsky Equation for a microecon class and positively no one was explaining why the derivative of the compensated demand function played out like it did. The sum of all the terms of the multivariable function was totally glossed over. This video clearly explained how each term is treated in a multivariable function, and I am incredibly grateful, because this problem has been seriously bothering me.
@ShirimeCid8 жыл бұрын
Hi Grant! I never noticed you were teaching on KhanAcademy. I'm a big fan of 3blue1brown videos and started to unravel the secrets of physics as an amateur. Thank you so much for this video, I always loved your way of explaining and am very exited to see what you will come up next. This video was just so great!
@3blue1brown8 жыл бұрын
+R3fini Thanks man! Do let me know once you've unraveled all the secrets in physics :)
@kushalpokharel34765 жыл бұрын
@@3blue1brown wow I have been seeing all the comments about you since the start of the series and woah you replied here. I know i am a little late to discover you but I am here after your linear algebra series and it's wonderful how many people love you and yeah I LOVE YOU TOO MAN
@sols8-ee7995 жыл бұрын
I really enjoy your videos! You have become my new favorite Math prof. =D
@kassymchurchman5511 Жыл бұрын
Thanks a lot. I hate simply following the formulas I don't understand the meaning of. This video made it clear!
@jakewaitze51046 жыл бұрын
Grant is back!!
@bhavna65656 жыл бұрын
Jake Waitze yay!!! Exactly
@oneinabillion6545 жыл бұрын
You are back finally. I've been watching.
@peppercanfly68883 жыл бұрын
this is equivalent to directional derivative of f(x, y) in the direction of the tangent vector of the curve traced by x and y, the formula in the green box is just ∇f ⋅ (dv/dt) where v = xi + yj
@lazer24055 жыл бұрын
This was great. I think a good application video would be the derivation of the Navier Stokes equation (or at least a portion of it) using this rule .
@shrinandhanbk94375 жыл бұрын
For a moment I was confused on how come 2*y is 2sin cos. Later I realized it to be small x :-). Neatly explained Thanks.
@user-ps4mu9dq4f6 жыл бұрын
Oh I just played this video only looking at its title, and I thought I was watching on 3blue1brown!
@dawne27802 жыл бұрын
I know this guy is a very accomplished mathematician but I still just feel safer when I hear Sal is teaching the lesson haha
@joluju23753 жыл бұрын
I wonder if ∂x in the denominator and dx in the numerator can cancel each other. I suspect maths purists will say it's incorrect to do so, but I feel it makes sense to do so, because it leads to a meaningful result that agrees with intuition.
@sumitgupta69054 жыл бұрын
Yay! Grant is back.
@Anteater236 жыл бұрын
So is the derivative of a multi variable function just the total differential divided by dt ?
@zakariaabdi18183 жыл бұрын
It's like nesting into a list using indexes in python. First index into the primary function, then index in to the secondary function within the primary function.
@dmt_benchpress1005 жыл бұрын
Best teacher ever - only this guy should do all the videos
@wanderingmage3553 жыл бұрын
After watching Sal writing in the last several videos, now I’m sure Grant is not writing with a mouse. 😆
@afnankhan303337 жыл бұрын
If f = x^2 + y^2 .. what will b the derivative of main function...w.r.t x and y
@cauchyschwarz32952 жыл бұрын
Would have been nicer to use an example where this chain rule is not an 'obvious' consequence of the product rule. Something like log(x+y).
@amineaboutalib Жыл бұрын
I agree
@mohammednaveed22105 жыл бұрын
You made it easy
@scholar-mj3om10 ай бұрын
Marvellous💯
@alagappan78187 жыл бұрын
If both X and Y are dependent on X isn't f a simple single variable function
@5231019976 жыл бұрын
Yes, but this is particularly useful in differentials
@kevinjackson9765 жыл бұрын
3Blue1Brown! No wonder his voice sounds familiar!
@isakwatz113 жыл бұрын
great!!!!
@agrimsingh0014 жыл бұрын
grant is back😀
@altuber99_athlete3 жыл бұрын
Holy frog, it's Grant/3B1B
@rogerramber76277 жыл бұрын
wait.. isnt this the guy from 3blue1brown?
@nickmilkshake26616 жыл бұрын
yes
@tascoVal6 жыл бұрын
I never usually comment but thank you.
@jeffersonhuynh941 Жыл бұрын
Grant Sanderson, I love you
@oksowhat2 жыл бұрын
you searched for it, it was not recommended
@MaryashrafBaly3 жыл бұрын
Wow!!!
@shawon2654 жыл бұрын
Yay!
@Manuel-pd9kf4 жыл бұрын
It's grant
@nishanagarwal60684 жыл бұрын
Hey Grant, What is the name of this software that is used for typing?
@abdomohamed49623 жыл бұрын
3blue1brown ... is it you ???
@alejrandom65923 жыл бұрын
yay grant!
@korwi73733 жыл бұрын
3b1b god
@xoppa096 жыл бұрын
which video is 3 blue brown and which is sal khan. please make two separate playlists.
@sgut19476 жыл бұрын
There again, please don't split it. This playlist has a great flow, and I've been learning loads from it. That we hear two different presenters is just fine. Thanks to both of you.
@That_One_Guy...4 жыл бұрын
Just look at the channel name for god sake
@quanghoang3801 Жыл бұрын
You cannot just give an example and then generalize it into a rule. I know that the Multivariable chain rule is correct, but we need rigorous proof.
@rando_guyАй бұрын
if you view del y and dy in a similar way, you can see they cancel out. and that goes for x too. (a similar method is used in differentiating single var parametric functions) in the end ur left with two rates of change (signifying the two dimensions) and we sum them up to get the final result you probably wouldn't call this a rigorous proof but it does generalize it