I love randomly stumbling onto Grant videos when learning with Kahn academy. Its like seeing a popular celebrity you like at a coffee shop even though you both live in the same city. You know it not unusual that he's there, but its still a nice surprise.
oh my god. this is the first time i saw ppl explaining chain rule this way. tho the image exits in my head i've never been able to draw it this clear!!!!!!!awesome!!!!!!!!!!!!
it's cool to see that the multivariable chain rule corresponds to the dot product between the gradient of f and the vector valued function derivative whose entries are the outputs of f
Thankyou so much all the time i am only remembering all the formula and i start to forget all. After knowing the core i can remember it for a along time thx!
The teacher from god... Really when people say that they don't understand math... the only reason they think so is because their teacher didn't manage to explain the whole logic behind some process... this was such an elegant way to establish the rule... it almost feels like you could have created this whole concept yourself and be a father of calculus in some sense
Those variables (x, y, and the function f) are dependent of t (their value are determined by t), so every change in t would surely cause some change in x,y,f (f is also dependent of x and y so change in x and y are added for change in f). They add linearly because of the dependancy of t and the fact that derivative is a linear operator. Something is a linear operator if following is true : L(c*F) = c*L(F) and L(F+G) = L(F) + L(G) (L = linear operator, F and G = some function, c = some constant)
Maybe a better way to explain this is that change in t is causing a nudge in f in the direction of v= dx/dt i + dy/dt j vector hence we find the direction derivative of f in the direction of v.
Grant, I am still not clear why the plus sign in between. f(x, y) could be anything, i.e. x*y, x^y, or (x^2)*(3y^3)+2xy, literally whatever. Why would the + sign maintain?
I believe it has to do with the fact they are independent variables (x does not depend on y) and as such we have we can add the partial effect of each one, giving us the total effect (variation of F(x(t),(y(t)) depends on x that depends on t and on y that depends on t. U add the individual effects and u get the total effect.
Can you not just simply say that the derivative of the funtion is the same as the product of the directional derivate with the directional vector being the derivative caused in the change of t?
I believe that you can, as the multi variable chain rule can be expressed as a matrix multiplication, and in some cases, this represents itself as a dot product.
I should start paying you guys 9k a year instead of my uni
Comment of the century right here. Woke af.
I love randomly stumbling onto Grant videos when learning with Kahn academy. Its like seeing a popular celebrity you like at a coffee shop even though you both live in the same city. You know it not unusual that he's there, but its still a nice surprise.
oh my god. this is the first time i saw ppl explaining chain rule this way. tho the image exits in my head i've never been able to draw it this clear!!!!!!!awesome!!!!!!!!!!!!
It is definitely a awesome way to look at partial derivatives chain rule.
I've been confused by the notation for a while and this cleared everything up instantly!! This channel is the best, thanks for everything!
“You can just cancel out the dts” haha sounds like a physicist
Omg! I always had this in my mind but you put it on paper so correctly & its so amazing man ! Hats off
Thank you very much! You help us see the beauty in calculus :)
it's cool to see that the multivariable chain rule corresponds to the dot product between the gradient of f and the vector valued function derivative whose entries are the outputs of f
Wow ! That completly changed my view!Thanks!
Thankyou so much all the time i am only remembering all the formula and i start to forget all. After knowing the core i can remember it for a along time thx!
That's the real way to explain it... Thanks!
You and only sal made sense of this topic to me
Yes this is great. So much more intuitive.
The teacher from god... Really when people say that they don't understand math... the only reason they think so is because their teacher didn't manage to explain the whole logic behind some process... this was such an elegant way to establish the rule... it almost feels like you could have created this whole concept yourself and be a father of calculus in some sense
thanks guys. This video just took the magic out of this concept.
Amazing explanation thank you!
I understood it intuively since the half of the video.
For those who wonder more strict representation of infinitesimal, watch 34th video of this list. He explained it more elaborately.
wait this is actually brilliant
How can you just add the individual nudges? How do you know that they add linearly?
Those variables (x, y, and the function f) are dependent of t (their value are determined by t), so every change in t would surely cause some change in x,y,f (f is also dependent of x and y so change in x and y are added for change in f). They add linearly because of the dependancy of t and the fact that derivative is a linear operator.
Something is a linear operator if following is true : L(c*F) = c*L(F) and L(F+G) = L(F) + L(G) (L = linear operator, F and G = some function, c = some constant)
I love you
thank you very much!!
This is also called the Total Derivative of a function 'f(t)' correct?
yes
WOW really nice thank you
Effing Legend mate
The cancelling out suggests that these two nudges are the same. Which they are not.
True, this is a poor analogy only helpful for memorization. But it's not the full picture
awesome!!
Marvellous💯
Thanks!!
Maybe a better way to explain this is that change in t is causing a nudge in f in the direction of v= dx/dt i + dy/dt j vector hence we find the direction derivative of f in the direction of v.
lot more intutive than bookish definition of matrix multiplication
sweet!
3 blue 1 brown crossover !!!
Thank you sir
NICE
Grant, I am still not clear why the plus sign in between. f(x, y) could be anything, i.e. x*y, x^y, or (x^2)*(3y^3)+2xy, literally whatever. Why would the + sign maintain?
I don't understand, what happen if I just use df/dx and df/dy instead of the partial one?
Thank you so much, 3b1b x khan academy!!
7:22 hey 3b1b!! you disappointed me there.
I'm a little lost , doesn't the equation df = (df/dx) * (dx/dt) * dt + (df/dy) * (dy/dt) * dt , translate to df = 2df, when you cancel out the terms!
The point in need of proof is that the products of the partials dot dx/dt and dy/dt are to be ADDED. And no hint is given here.
Have to agree
Indeed. He just snug the plus sign in without even mentioning it. And is the crucial part... bad.
I believe it has to do with the fact they are independent variables (x does not depend on y) and as such we have we can add the partial effect of each one, giving us the total effect (variation of F(x(t),(y(t)) depends on x that depends on t and on y that depends on t. U add the individual effects and u get the total effect.
I would think that was obvious though.
@DnB and Psy Production Thnx.
hey is that the same guy as 3blue1brown, or does he just sound similar?
Indeed, is the same
@@agustinmiranda3989 Good to know. Thanks for answering
But dy/dt or dx/dt ARE fractions, they are infinitesimal fractions, they are the infinitesimal and indivisible part of a magnitude Δy/Δt and Δx/Δt.
It sucks when each components of function i.e. f(x) f(y) and f(z) are function of x,y,z,t ,😫
Why?
@@satyamprakash7030 I don't remember why I posted that comment
Can you not just simply say that the derivative of the funtion is the same as the product of the directional derivate with the directional vector being the derivative caused in the change of t?
you mean dot product?
I believe that you can, as the multi variable chain rule can be expressed as a matrix multiplication, and in some cases, this represents itself as a dot product.
5:38 did you just say constant? :c *sobbing function noises*
The trouble with your videos is that it becomes impossible to look at other maths videos...
"""lego batman meme"""
700th like
Hmm I think Patrick did it better.🤔