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Partial derivatives and graphs
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- เผยแพร่เมื่อ 10 พ.ค. 2016
- One of the best ways to think about partial derivatives is by slicing the graph of a multivariable function.
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1:55 the thing my toilet sees everyday
Oh man ,u see things differently
Which normal persons can't visualize
This is art.
Can't even think of a better way of explaining this. Thank you!
These videos make me happy to learn! ^_^
Good to hear! Me too.
Great video, my only little remark is that the way you write your twos makes them look a lot like a z, which would be fine in the single variable world, but since we are working with functions in three dimensions, it could be confusing for some people.
If someone thinks that is a Z in this context then lmfao
You made my last 10 years man...
No word to thank you...
❤️❤️❤️❤️❤️❤️❤️❤️❤️
This man is the Bob Ross of math!
I have been struggling with this for a long time and in 2 videos you make it so clear and understood thank you so much
What software do you use for writing notes and slicing graphs?
thank you.. i had the intuition that the partial derivatives would form 'slices' of the surface to form curves, i just had such trouble visualizing it in my mind.. i also did not realize to form these slices you just have to pick a constant value for y, as you increment the constant value you can start to visualize the gradient of the function..
Love the explanation and the graphics.
Wow!! What an amazing explanation...!!!Gr8👍👍👍👍👍👍👍👍👍👍👍👍👍👏👏👏👏👏🏻👏🏻👏🏻👏🏻👏🏻👏🏻👏🏻👏🏻👏🏻👏🏻👏🏻👏🏻👏🏻👏🏻👏🏻👏🏻👏🏻
Thank u for making it so simple
before watching this video i had never seen a graph in such a way
Is this 3blue1brown?
Love the graph "slicing" ! 😂 🎉
you could have used small angle approx to denote the trig values
What a great explanation.
So the partial derivative only shows a change in Z because x or y,
(depending on whose partial derivative you take) will be constant?
Perfect explanation
What about when you want to know what the shape is doing in a partial step in the x direction and a partial step in the y direction?
Super cool video!
My mind was blown when I got to know that this is 3blue1brown
Thanks so much! This helped!
Why we are interested in 2 specific derivatives in specific directions (along the x and y axes) when we can ask about the derivative of other infinite directions? is it because it is easier to calculate? how can we calculate the derivative of other directions?
The different directions would be different parametrisations of the same graph, but lead to a different function.
It is easier to calculate in x and y directions as usually we are in euclidean space. We can surely calculate the derivative in any direction we want, for example by using polar coordinates here the parameters would be the angle theta and the radial direction in which we want to calculate, this is particularly useful when there is spherical symmetry, but it is really tedious
Can i say,wow!what a great job!
Great job 👍👏🎉
Beautiful!!!!❤️❤️
Thank you!
Thank you so much
You are awesome!♥️♥️♥️♥️🙏🙌🙌🙌🙌
graphs are the best
Very good editor you use there. I don't believe it is SmoothDraw 4? What program is this?
Really best videos
4:46
x youre a constant!
why?
youre the variable!
good explanation
Great♥
Beautiful!!
Awesome
Good video
What doesn't make sense is if you use a pure graphical interpretation. What is stopping you from looking at the slope from the other direction and thinking what should be positive is actually negative?
How to evaluate the derivative in any direction but not in direction of x or y axis
directtional dedriative
Thanks I did understand d concept. But how did u locate tat point(-1,1) to on graph?
same question for me
The first graph in the video is like man body upside down
You sound like timothy sykes
But it's Grant Sanderson of 3Blue1Brown! Isn't it?
Yes it is.
But sel Khan is best all the time ..
and what does fxx and fxy mean in geometry?
does anyone know what program they are using to draw? it doesnt look like the usual smoothdraw
its the grapher
isnt this 2 variable input and 2 variable output? why does he call it 2 variable input and 1 variable output?
what is the name of the program used in 3d drawing ?
Interesting. I like to know too. I don't believe this is Smoothdraw 4.
Mac Grapher
why is f(x,y) in 3D?
Sai Meghana f(x,y) isn't actually in 3d.
The point is the inputs are ordered pairs(as opposed to usual functions from |R->|R)
So the "graph" is made like this considering the input domain to be the whole of |R^2
f(x,y) is in three dimensions, if we graph it the standard way. Two dimensions for input (x,y) and a third dimension z where z = f(x,y) for output.
I have to do this shit in uni? Fuuuck
it's actually pretty interesting.
What you mean? There's alot of money involved in machine learning? Doesn't it reduce human labour?
Alpha Beta nah , people who work on machine learning gets more money , people who work for learned machines gets less money.
what software did u use?
LOVE YOU WHOEVER DISLIKED THIS MUST BE BLIND
Oh 3b1b.
I thought so
Thank you! Does anyone know what is this program? it looks really useful..
It’s called Grapher and its a default program on Mac computers made by apple
@@ijarbis187 No, its manim. An open source python library
shouldn't the point (-1,1) be parallel to the (x,y) surface?
I guess, Mr Grant Sanderson speaking 🙄
Can you please tell me the plotting software used
It’s called grapher and its a default program on Mac computers made by apple and its only on Mac I’m pretty sure. It’s amazing I use it all the time.
@@ijarbis187 Its manim. He makes the program himself
maaaaaaan
why is this a 3D graph? shouldn't it be 2D?
f(x,y) is a 3D graph because x and y are the input and f(x,y) is the output.
I personally don’t believe in god but when I think of a person who does deeds Jesus would do i would think of grant
second !!
oversimplified
how would you explain it?