Formal definition of partial derivatives
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- เผยแพร่เมื่อ 10 ก.ย. 2024
- Partial derivatives are formally defined using a limit, much like ordinary derivatives.
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It's super cool to listen to 3b1b in this sort of live format))
Difficult to remember to put "like" to all videos. Amazing teaching.
Oh my god 3blue1brown
Drew M-R wait what?😳
That h notation is really just there to cause confusion. Thank you for pointing out what it really just it.
This voice sounds very familiar...
This is my favourite video in the series. Somewhere along the way I thought I was catching glimpses of the secrets of the universe...
thanks for spreading the knowledge
Thank you so much for these incredibly valuable explainations that help us not only understand but also get a real feel of the difficult and complex concepts of calculus. This level of understanding of the concepts even most maths professors dont have, and what they teach is nowhere near to what we can learn from here.
When he wrote the limits, he didn't extend the fraction signs for the entire numerator... It should include all of [F(a+h,b) - F(a,b)]. I hope no one was confused by that.
Thanks
Ty
Thank you for the explanation!!!!
I love your videos. With your videos I do believe anything can be learned.
at 0:55 f(x) gets prettier as the value of x increases
Whenever I hear that voice, I know I'm going to learn some _real math!
WE LOVE YOU GRANT SANDERSON!!!
HE IS TOO SMART
totally agree! Last night, i saw a video on Lev Landau, he had mastered the department physics maths and chemistry at age of 14.. I suspect this guy has mettles of Lev Landau which is obviously rooted in his simplicity of thought.
SPOILER: oh Jesus, I cannot believe the word maths got a red line under it when i typed in the comment!
sounds familiar... mr pi!
Thank you very much
Thank you for clarifying ...great explanation! 🎉
Grant for the win!
Good job.
Really interseting approach of interpreting the derivative 5:13
Ty
Great!
I think Khan Academy deserves the 400 bucks I paid my school for Calculus 1.
Why is h used for a nudge in the x direction? I suspect it is related to the use of (h, k) to represent the image of the origin for a geometric transformation. The variable h is used there as well for a shift in the x direction.
It's( x+h)-x
"room for rigour"
Funny phrase right
best of luck
ITS GRANT SANDERSON!
how can i find out which playlist is this video from ?
It's from "Multivariable Calculus"!
3b1b is that you?
(a, f(a)) and (b, f(b)) are points on the graph x^2 and h = b - a, solve for b, b = h+a, then (a, f(a)) and (h+a, f(a+h)). slope = f(a+h) - f(a)/h
you could start this from about 7 minutes and go from there, refer to prev lessons will save time. also, could mention that the new thing is each value (x,y,z, i,, j, k...) just becomes a function, after that its all familiar but now for n dimensional geometries
Shouldn't the partial derivative be "del" not "d"?
Moses Stevens some calculators don't have "del" function
Which is y people can use normal derivatives to do this one variable at a time
So if people wanted to do it on a calculator, they can use normal derivatives to find partials
The issue is more one of pronunciation - the symbol is "del" not "d", isn't it? :)
Ya it's del
cheese is from cow
that's true
@@MrOhWhatTheHeck You are right
@@satyamprakash7030 how could you say something so controversial yet so brave?
first
+Crossfire Memer edgy
Crossfire Memer I tried
Sorry, but Grant takes 10 minutes to explain something that Sal can do in five minutes. When you go into that much detail it tends to get muddled.
I agree. Even though I'ma big fan of Grant's work at 3b1b where he intuitively explains concepts with animations, I also think there is need for a certain rigorousness while formally teaching something. You get to the concept easily.
At least he doesn't take an hour or more like most lecturer does, it's annoying af
It's okay everyone has different teaching styles.
Grant's teaching philosophy is always to elaborate the intuition of the mathematical concepts that we are already familiar with.