Symmetry of second partial derivatives
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- เผยแพร่เมื่อ 4 ต.ค. 2024
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There are many ways to take a "second partial derivative", but some of them secretly turn out to be the same thing.
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Oh man, this voice. Greeting 3blue1brown
Thanks a lot for those two intro videos on partial derivatives, now I finally understand that what is a partial derivative both graphically and algebraically.
I'm a high school student just
I highly recommend you to not miss any of the last 3 videos before watching this.
Could you plz analyze this fact with graph, excellent lectures.
MAAN! You're an artist. I cannot thank you enough.
+3Blue1Brown is it you?!
Derek Witzig yeah it is him :)
I immediately recognized his voice lol
@@renzpaoloogena1900 Yup,me too
Hi Mr., could you please explain that theorem which says that mixed partials are not always equal?
satz von schwarz
Please give a intution on second order partial derivatives
This may not be the best explanation you ever hot however I will try my best. When we take the first derivative we are essentially asking what's the rate of change of the point to the point just slightly ahead of it. That's why it is df/dx, the df represent the change in function per the small dx change in the input value. When we say take the double derivative we are essentially asking what's the rate at which the rate of change changes. For that we have to take df(df/dx)/dx. In this scenario we are essentially taking the square of the tiny change in function and then dividing it by the square of the tiny change in the input value, that's why we got (df)2/(dx)2. Writing it like df2/d2x, in my humble openiun is just a matter of preferences.
Grant for the win!
The cartesian refraction notation is partial by constant in diverse expression using dispersion in velocity to the quantities medium also geometric internals can concave convex bisector Abberation on filgment construct using ratio good luck
thanks for perfect explanation
thankssss))))))))))))))))))))
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Perfect
THX from Thailand
hello iM from Thailand too))))))
Watching this without ads
I think youtube is gonna blow up
Can you pls do some videos for 3+ variable functions ? I'm really struggling
What should i learned to understanding this lecture help me!!!!!
you explained it so clean
COOL!
I believe it, but why?
Why didn't you take the second partial derivative of sin(x)(2y) at 5:33?
because it's easy for you to make
treat x as a constant, since it's multiplying, it continues to be sin(x)
do a derivative of 2y and it's equal to 2
so 2sin(x)
Your tone puts me at ease with topics that would otherwise scare me off
cheers mr 3b1b
Excellent!!! Lots of love
Marvellous💯
oh shit!! its my boy 3b1b
But are partial derivatives commutative?
Excellent explanation! 😂
but why is this always true?? Is there anywhere I can go to get the intuition behind it?
This is not true in general. Consider the example f(x,y)=xy \frac{x^2-y^2}{x^2+y^2} if (x,y)≠(0,0) and f(0,0)=0. You can find fyx(0,0)=1 and fxy(0,0)=-1.
In fact, fxy (x0,y0)=fyx (x0,y0) if f(x, y) and its partial derivatives fx, fy, fxy
and fyx are defined in a neighborhood of (x0, y0) and all are continuous at (x0, y0)
That exact example is given on the Wikipedia page on the topic:
en.m.wikipedia.org/wiki/Symmetry_of_second_derivatives
He didn't completed the pyramid. :(
Bro❤
ts not fx or unf. not all purpox intex,notnex
Please don't take trigonometric examples man.
Why😂
Golly
hiii
first
Bruh just use X and y as examples not sin💀
Don't make it hard people. the first derivative is the slope of the tangent line, or the instantaneous speed, and the second derivative is the acceleration.
What is the nth derivative?
This is multivariable calculus.
It's partial differentiation equation my man
And what is the meaning of 2nd partial derivative ?
I mean ... 1st partial derivative shows us a change of our function in certain direction, right?
What 2nd derivative shows us?
Thanks
fxx is the concavity of f , in the x direction. And fyy is the concavity of f , in the y direction.
It's the rate of change in the rate of change of a variable.
Think change in acceleration.
The first partial derivative tells us the slope on the plane perpendicular to the x(or y)-axis, and The derivative of that ,which is the second partial derivative tells us the curvature on the plane perpendicular to the x(or y)-axis.(by the way, I’m 10 years old and I’m not lying)