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

@afterbunny257

5 жыл бұрын

Yeah, 3Blue1Brown and thumb!

@fanimeproductionst.v.3735

5 жыл бұрын

r/ihavereddit

@meowwwww6350

3 жыл бұрын

300th like

@MFedoseyev

3 жыл бұрын

@@meowwwww6350 thanks for the reminder man

@meowwwww6350

3 жыл бұрын

@@MFedoseyev ya

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 = then (∇f dot u) = a*(df/dx) + b*(df/dy).

@morganyu3391

4 жыл бұрын

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

@nikhilnegi9446

4 жыл бұрын

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

@NovaWarrior77

4 жыл бұрын

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

@anjannayak7360

3 жыл бұрын

Can you please answer Nikhil Negi's question

@anjannayak7360

3 жыл бұрын

@@nikhilnegi9446 did you figure out?

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

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.

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

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

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

@14tim4

7 жыл бұрын

Eirik Skogstad Andreassen is it?!

@gabormarcellmolnar1987

7 жыл бұрын

he probably is

@Fatherzakariah

7 жыл бұрын

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

@sarahvan3826

6 жыл бұрын

Eirik Skogstad Andreassen Omg exactly my thought

@satyakighosh4226

5 жыл бұрын

me too lol

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

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

@Dularish1993

4 жыл бұрын

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

4 жыл бұрын

"V × h" why is it like that

@mfadhilal-fatih1427

4 жыл бұрын

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

4 жыл бұрын

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

@kaustavgoswami1998

3 жыл бұрын

Find your gradient, thats the way to ascend.

Muito obrigado, rápido e claro. Melhor impossível

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

Жыл бұрын

Did you become rich?

@noahagnew6517

Жыл бұрын

@Arijita Sarmah working on it.

@arijitasarmah4864

Жыл бұрын

@@noahagnew6517 great! Keep it up!

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

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

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

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

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)?

Happily surprised to hear 3blue1brown in a khan vid

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

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

Жыл бұрын

3Blue1Brown

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)?

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

Thank you!

Thanks!

Thank you. Thank you. Thank you.

Excellent explanation, thank you so much

this is awesome explanation, i'm very impressed

nice thx thx u are a life saver

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

@fanimeproductionst.v.3735

5 жыл бұрын

*Mega Nut*

awesome explanation!!!

Thank you so much.

Fantastically explained

Thanks Grant, still six years on!

awesome!

Awesome video

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

@232sumanth

4 жыл бұрын

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

2 жыл бұрын

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

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

I like the"nudge" analogy! 😂

Marvellous💯

GREAT VIDEO

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 ?

You are great

So good!

explains idea of steepest ascent

what a beautiful voice

That's pretty neat.

@alechewitt2347

7 жыл бұрын

hahahahaha, how neat is that?

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?

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

This is goood

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

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

When I hear that voice , I know I am safe

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

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

Why do these have so many dislikes?

@bobbobson2061

8 жыл бұрын

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

7 жыл бұрын

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

6 жыл бұрын

+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

5 жыл бұрын

They probably don't like math

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

@ConceptualCalculus

3 жыл бұрын

Yes,

Grant sanders I love you

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

7 жыл бұрын

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

7 жыл бұрын

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

@xoppa09

6 жыл бұрын

I agree, it should be unit vector

@xoppa09

6 жыл бұрын

but why should it only be df?

@ayonbiswas4186

4 жыл бұрын

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.

This voice😃

Came from 3blue1brown's neural network series

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.

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

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

4 жыл бұрын

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...

4 жыл бұрын

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°)

Is this @3Blue1Brown ?

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

5:26

Doesn't w have to be a unit vector?

@gigo518

6 жыл бұрын

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.

some say that Grant still nudging nowadays

Love you 3 blue 1 brown

I am a simple man . Seemed 3B1B ish

@josephlee392

5 жыл бұрын

It is him.

2:09

yea wheres sal

Jinder Mahal Vs Brock Lesnar

Why don't you just do an example problem?

Is this a Gateux derivative?

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.

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

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

2k19 Like here

Uhhhh.. what?

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

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

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

@Mr46ser

7 жыл бұрын

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

@citiblocsMaster

6 жыл бұрын

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

well im screwed

Is this 3blue1brown

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)!

"Itty bitty bitty bitty"

Money

I did not understand

really really really small

what happened to the original khan voice? :(

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.

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

sir you are speaking too fast to follow

@gigo518

6 жыл бұрын

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...

He sounds like the guy from 3blue1brown

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

@whitewalker608

5 жыл бұрын

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

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