Directional derivative 

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

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).

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 😍

When I hear that voice , I know I am safe

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

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

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

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

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)?

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

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

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

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

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)?

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

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

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 ?

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

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

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

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

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

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

Muito obrigado, rápido e claro. Melhor impossível

Happily surprised to hear 3blue1brown in a khan vid

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

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

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?

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

Excellent explanation, thank you so much

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

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

Thanks Grant, still six years on!

I like the"nudge" analogy! 😂

this is awesome explanation, i'm very impressed

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

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.

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.

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

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

Thanks!

Thank you so much.

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

Thank you. Thank you. Thank you.

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

Awesome video

Thank you!

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

Fantastically explained

Doesn't w have to be a unit vector?

some say that Grant still nudging nowadays

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

explains idea of steepest ascent

Marvellous💯

what a beautiful voice

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

Is this @3Blue1Brown ?

Why do these have so many dislikes?

GREAT VIDEO

Is this a Gateux derivative?

2:09

You are great

This is goood

awesome!

nice thx thx u are a life saver

awesome explanation!!!

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)!

Why don't you just do an example problem?

5:26

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.

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

I am a simple man . Seemed 3B1B ish

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

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

Came from 3blue1brown's neural network series

So good!

This voice😃

Grant sanders I love you

Love you 3 blue 1 brown

That's pretty neat.

Jinder Mahal Vs Brock Lesnar

yea wheres sal

Is this 3blue1brown

Uhhhh.. what?

really really really small

2k19 Like here

well im screwed

Money

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

"Itty bitty bitty bitty"

He sounds like the guy from 3blue1brown

I did not understand

what happened to the original khan voice? :(

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

sir you are speaking too fast to follow

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