Directional derivative

Directional derivatives tell you how a multivariable function changes as you move along some vector in its input space.
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[@MFedoseyev]

I am a simple man. I hear 3Blue1Brown, I upvote

[@afterbunny257]

Yeah, 3Blue1Brown and thumb!

[@fanimeproductionst.v.3735]

r/ihavereddit

[@meowwwww6350]

300th like

[@MFedoseyev]

@@meowwwww6350 thanks for the reminder man

[@meowwwww6350]

@@MFedoseyev ya

[@priyankkharat7407]

Thank you so much for giving an intuitive understanding. We already have a lots of material on the internet with it being 100% formally correct with all the notations in place. But I feel it becomes too cluttered and difficult to understand in the first couple of tries, and becomes little frustrating. Khan academy has struck a correct balance between use of notations and bringing an intuitive sense to it, so it doesn't become too much for a complete beginner like me. Thank you Sal and 3blue1brown.

[@not_intrested]

😭 I don't understand how could someone be so perfect in making complex stuffs feel as a piece of cake 😍

[@SelvesteDovregubben]

Wait a minute... Isn't this 3Blue1Brown?

[@14tim4]

Eirik Skogstad Andreassen is it?!

[@gabormarcellmolnar1987]

he probably is

[@Fatherzakariah]

I just jumped down to post the same comment! I was so excited as soon as I heard his voice!

[@sarahvan3826]

Eirik Skogstad Andreassen Omg exactly my thought

[@satyakighosh4226]

me too lol

[@Raikaska]

Wow. That makes the dot product of the directional derivative much more intuitive! Thanks

[@noahagnew6517]

If i ever become rich I'm donating a large sum of money to Khan academy cause without them I don't have a chance

[@arijitasarmah4864]

Did you become rich?

[@noahagnew6517]

@Arijita Sarmah working on it.

[@arijitasarmah4864]

@@noahagnew6517 great! Keep it up!

[@Adhithya2003]

When I hear that voice , I know I am safe

[@prashantpant2876]

I am lost in Gradient. Somebody please give me a direction.

[@Dularish1993]

A gradient vector points in the direction of greatest slope. Now suppose we need the slope in some other direction. So for this need, we use the property of dot product, so we simply dot product the vector with gradient, so we get the slope in the direction of the vector(multiplied by magnitude of vector). Now lets say we have a unit vector which already points in the direction of gradient(that is the direction of greatest slope). If we dot product that unit vector with gradient, we could get the maximum value than it would have been possible if we had any other unit vector pointing to any other direction.

[@mfadhilal-fatih1427]

"V × h" why is it like that

[@mfadhilal-fatih1427]

V is the vector for looking x y plane in different 1d way (not only according to x or y). V*h means that how much is h (on the v vector way) for h on the x and y plane way

[@nikhilnegi9446]

Dularish Kuttuwa How can the directional derivative depend on the vector w Instead of vector w, their should be unit vector w.

[@kaustavgoswami1998]

Find your gradient, thats the way to ascend.

[@hunarahmad]

this was very helpful for me to understand machine learning. Thanks

[@jamescalo9276]

Am I the only one who thought this was Sal Khan's Voice? Every Khan academy Video I've ever watched has been Grant in disguise! I cant tell what's more mind blowing; this or finally understanding gradient decent (I've been lying to myself for 7 years)?

[@fosheimdet]

But with this definition of directional derivative, the value calculated will be dependent on not only the direction of the vector, but also the norm. So if you take the same vector, multiply it by 2 and find the directional derivative, it may very well give you a totally different number. Why not just divide both terms in the definition of directional derivative by one of the components of the vector to consistently give the same directional derivative for a vector pointing a certain direction (regardless of its norm)?

[@aristotleplato7330]

man.. i love this guy. he should open a youtube channel of his own and maybe.. teach stuff with animations if he knows how to make those

[@christopherbanda418]

3Blue1Brown

[@cooper7655]

For those who are a little confused about the difference between the gradient and the directional derivate: In the case given in the video, the gradient is a vector whose components are scalars, each representing the rate of change of the function along the standard unit vectors of whatever basis being used (A lot of the time it’s the Cartesian plane and the unit basis vectors are i j and k). The gradient only tells us how the function is changing with respect to the axes of our coordinate system, but it’s hardly the case that our mathematical interests lie solely on the axes of our coordinate system, therefore we need the directional derivative. The directional derivative is a scalar value which represents the rate of change of the function along a direction which is typically NOT in the direction of one of the standard basis vectors. In conclusion, if you want to find the derivative of a multi variable function along a vector V, then first you must find a unit vector in the direction of V, called u, and then take (∇f dot u). If u = < a, b > then (∇f dot u) = a*(df/dx) + b*(df/dy).

[@morganyu3391]

Thank you so much for this, cleared a big question i was looking for on KZbin

[@nikhilnegi9446]

Cooper Stevens How can the directional derivative depend on the vector w Instead of vector w, their should be unit vector w.

[@NovaWarrior77]

Thanks for your commitment to improving the internet with quality commenting.

[@anjannayak7360]

Can you please answer Nikhil Negi's question

[@anjannayak7360]

@@nikhilnegi9446 did you figure out?

[@trendypie5375]

i have a little confusion about the fact that why adding the rate of change of x component and y components lead to the rate of change along the vector ?

[@jefwowes1607]

This is much better than similar videos I have seen a couple of years ago! Thanks.

[@lefebvre4852]

It's incredible how 7 minutes of a good video can fix one hour of incomprehensible lecture of a bad professor. Thank you.

[@ushiocheng]

after 10 min of my teacher try to Illustrate this concept, I eventually can't withstand it and go straight to youtube to look up the concept 4min into the video, I got : what it is, how to calculate it, and why is it useful. Also it is not that my teacher is bad, just I am good at abstract concepts and have taken all the ap physics

[@muskankushwah8406]

Literary so amazing videos , it had clear all the things more explicitly

[@Eltodofull]

But doesn't the vector in that dot product have to be a unit vector?

[@322luisao]

Muito obrigado, rápido e claro. Melhor impossível

[@winstonvpeloso]

You have to normalize the direction vector, no???

[@ConceptualCalculus]

Yes,

[@professional2094]

this is awesome explanation, i'm very impressed

[@ΚωνσταντίνοςΛαζαρίδης-ξ9ι]

Thanks!

[@mercedes9474]

Fantastically explained

[@NovaWarrior77]

Thank you!

[@232sumanth]

I expected Grant to give intuition on why a directional directive is simply a sum of the partial derivates ? I did not get this part of simply adding up the increments in f. Can someone help

[@adityaprasad465]

Directional derivative is not simply a sum of the partial derivatives. You can think of it as a *weighted* sum, though. You multiply how much you would change (per unit) in each direction, by how much you actually walk in each direction. For example, if w = (a, b) then we walk *a* units in the x direction and *b* units in the y direction.

[@That_One_Guy...]

Directional derivative is a scalar value simply telling how much the small step along (x,y) is affecting the height/z value, it's a dot product between gradient and some random vector that you choose and want to know how it affect z value (the v/w vector) (that's why it's the "sum of partial derivative" as you said), dot product is telling you how much a vector is pointing in the same direction of another vector, If vector v/w is happen to be in the same direction as the gradient itself then it tells you the direction to get maximum z increase is in the direction of gradient, because it gradient dotted with the gradient itself (and there's the fact that there's cos term which max out when the angle is 0°)

[@medhavimonish41]

please write 2 in a way so that it look like 2 not Z

[@viniciush.6540]

what a beautiful voice

[@RoyalYoutube_PRO]

So... a standard derivative is a directional derivative from negative to positive in that dimension...

[@tommasopalamenga9184]

Don't you also have to normalise the vector to be equal to one before multiplying it by the gradient?

[@JJ_san]

I don't understand why is it a scalar value when we r finding the directional derivative. What does it meant by that scalar vaue? I thought that directions have to be vectors.

[@scholar-mj3om]

Marvellous💯

[@ViciandoCodigo]

Is this @3Blue1Brown ?

[@danieljaszczyszczykoeczews2616]

GREAT VIDEO

[@p.z.8355]

Where is the directional derivative used ? I though the gradient points into the steepest direction, so why bother finding other directions ?

[@pr1ckastley]

Doesn't w have to be a unit vector?

[@gigo518]

It doesn't have to be. Some texts define the dir. der. using the unit vector, others do not. So it depends on the definition your textbook or course wants you to use.

[@yashwanthpurli3946]

awesome explanation!!!

[@judahdsouza9196]

2:09

[@NicolasDiazWahl]

Why do these have so many dislikes?

[@bobbobson2061]

People with such a sense of entitlement that they throw a tantrum when the free education they receive from a knowledgable teacher isn't presented by the guy they're used to.

[@darrenyoungal4902]

Best part about this is I find this guy's videos (think he's called 3blue1brown) infinitely more helpful than Khan's. Not that Khan's are bad but I just prefer 3blue1brown's explanations. He also programmed his own visual software that he uses in other videos and it's amazingly helpful.

[@Postermaestro]

+RedRussianRages! No it's a great introduction to directional derivatives. Check out his video on "Directional derivate, formal definition" where he explains the reason for using the unit vector. These videos aren't about feeding you formulas to put in your cookie cutter exams to pass, but to understand the derivations from the bottom up.

[@suhuyinimohammedaminimoro8346]

They probably don't like math

[@mansour9591]

Sal khan i need you now I cant understand this person at all

[@weibin4283]

nice thx thx u are a life saver

[@인바디-r9c]

awesome!

[@vedanshkakkar4415]

Why don't you just do an example problem?

[@mihai5085]

This is goood

[@حسينمحمد-ف4ظ8ن]

Tabark 👩🏻‍🔧: Function F=(10/(sinx.cosx+z²))¼ Point P=(1,2,3) direction a=i+3j+2k

[@cscsun3796]

5:26

[@blockbusstar]

Who are you and what have you done to sal !!!

[@Mr46ser]

Doesn't matter, him and Sal are both great!

[@citiblocsMaster]

I think as teachers Sal and 3Blue1Brown are the tippy top

[@benzmansl65amg]

So good!

[@hqs9585]

How can you dot two matrices, ( 1 column and 2 rows ) X ( (1 column and 2 rows)? Th number of columns of first matrix (vector) needs to be equal to thge number pf rows of second vector ( matrix). Otherwise the product operation is IMPOSSIBLE)!

[@gurukirans266]

Love you 3 blue 1 brown

[@paulisacat]

yea wheres sal

[@hyunwoopark9241]

I am a simple man . Seemed 3B1B ish

[@josephlee392]

It is him.

[@effy1219]

great video but i think it will be even better if you can focus on explaining the core line of knowledge, avoid explaining the notation, little bit distraction for new learner. for new learner, the priority thing is to grab the main knowledge frame.

[@asdfasdfuhf]

Came from 3blue1brown's neural network series

[@ribhav99]

Grant sanders I love you

[@Sigma1907]

2k19 Like here

[@HSelimSerdar]

really really really small

[@Qq-lp5xg]

That feeling you get when he writes a vector function as a 1x2 matrix 😵

[@chendwachintu4429]

what happened to the original khan voice? :(

[@e.josesutama6842]

He sounds like the guy from 3blue1brown

[@samaramar2662]

sir you are speaking too fast to follow

[@gigo518]

You can slow it down with the speed setting. Click the gear icon and try .75x or .5x speed. Personally I like playing these at 1.5x speed, so I don't think he talks too fast...

[@aman2426]

You are going too fast. Feels like I am back to school, not khan academy.

[@drewpierpont3361]

This guy is good too, but I just wish he was as intelligible as Sal. His voice could use some extra processing.

[@whitewalker608]

Go see 3blue1brown. You'll realize the difference between him and Khan. He's from Stanford. People are averse to change that's it.

[@Imaroster]

You are not like Sal....very bad explanation...

[@guilhermefranco2949]

some say that Grant still nudging nowadays

[@douglasmangini8744]

"If you look at this expression, it looks like a dot product", said Grant for the nth time by now

[@sameerpurwar4836]

sir, i think the vector should be unit only then can we use the notation df/dv, in your case it should be only df

[@jerklecirque138]

Good catch. You're correct that the vector should be unit length. If it were not the case, then you and I could compute two different directional derivatives even though our vectors point in the same direction (but have different lengths).

[@Raikaska]

Sameer Purwar yep. That way it would be consistent with the dot product computation

[@xoppa09]

I agree, it should be unit vector

[@xoppa09]

but why should it only be df?

[@ayonbiswas4186]

But if the problem is not about a unit vector (when it is not about just the direction), we need to compute change about the total vector, then this is totally justified.

[@mayureshjoshi4616]

thanks grant ! you are the one that's making math intuitive and fun for me .....

[@miguelbguaita]

Hi! Just one question, has the vector v to be normalized? Otherwise, it would scale the resoult by the magnitude of v, or am I wrong?

[@diegmaindangerous6819]

Mega nut, its ya boi 3 blue 1 brown back at it again with the cleanest calc lessons

[@fanimeproductionst.v.3735]

*Mega Nut*

[@nikhilnegi9446]

How can the directional derivative depend on the vector w Instead of vector w, their should be unit vector w.

[@happyd6145]

Jinder Mahal Vs Brock Lesnar

[@user-cm7sq4rw5j]

4:27 Can anyone tell me why he -fx(x,y) plus 2fy(x,y)?

[@lucajones2349]

Grant, how are you so good at teaching this stuff intuitively?!

[@maxbaker3370]

Is this 3blue1brown

[@frederikbrokbrandi917]

Is this a Gateux derivative?

[@yadpreetcheema4806]

what's with all the dislikes, this was by far the best explanation I could find

[@232sumanth]

Reason for dislikes -> I expected Grant to give intuition on why a directional directive is simply a sum of the partial derivates ? I did not get this part of simply adding up the increments in f. Can someone help

[@brechtxt8096]

Good times, when you could actually see a videos' dislikes

[@mathijsjacke1915]

@@232sumanth ikr

[@nickdavis8556]

Uhhhh.. what?

[@justho3350]

well im screwed

[@karthik-ex4dm]

Awesome video

[@Potencyfunction]

My last level in math was B but we didnt had derivatives...we had differential functions. Totally hard at brains, slow learning as is not my language math.

[@NehaKumari-tl1by]

Is there any other video of 3blue1brown in other you tube channels...I need it really..🥺🥺🥺

[@KIMHWANHEE-v5s]

we got korean captions here which is so great for me cause i can barely understand english

[@tunanimo1789]

Excellent explanation, thank you so much

[@AlexLectures]

Thank you so much.

[@Postermaestro]

so great in combination with the video on the formal definition and the one relating the directional derivative to the slope

[@curtpiazza1688]

I like the"nudge" analogy! 😂

[@AidanHomewood]

Thanks Grant, still six years on!

[@seanguo9366]

explains idea of steepest ascent

[@jeffgalef121]

The part with h really threw me off. The dot product explanation was much more helpful.

[@komalvenkatesh4527]

Thank you. Thank you. Thank you.

[@j.j.b.13]

I did not understand

[@jmelojr]

You are great

[@AkashChauhan-co3ym]

This voice😃

[@BennettAustin7]

Money

[@SergioRodriguez-iz7of]

That's pretty neat.

[@alechewitt2347]

hahahahaha, how neat is that?

[@dariomiric2958]

"Itty bitty bitty bitty"

[@DuctTapeRapist]

Happily surprised to hear 3blue1brown in a khan vid