Question

In second derivatives of f(x,y), why is\[ f_{xy} =f_{yx} \]

Answer 1

@SmoothMath @experimentX

Answer 2

seriously ... i haven't worked it out till now!!

Answer 3

\[ \frac{\delta }{dx} f(x,y) = \lim_{\Delta x \rightarrow 0}\frac{f(x + \Delta x, y) - f(x, y)}{\Delta x}\]
\[ \frac{\delta^2 }{\delta y \delta x} f(x,y) = \lim_{\Delta y \rightarrow 0}
\lim_{\Delta x \rightarrow 0}\frac{f(x + \Delta x, y + \Delta y) - f(x, y+\Delta y)}{\Delta x} \\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; - \lim_{\Delta x \rightarrow 0}\frac{f(x + \Delta x, y) - f(x, y)}{\Delta x}

\] The whole by delta y ... sorry unable to write it in latex.


If you try to calculate dxdy <---- you can show the same result

Answer 4

Okay thanks! One more quick question, how do I write partial curvy d in LATEX?

Answer 5

\delta for \( \delta \)
\Delta for \( \Delta \)
and my secret technique ..

Answer 6

Thank you so much!! ^^

Answer 7

if you have firefox ... right click on latex equation .... -> "show math as" -> "Tex Commands"

Answer 8

You just made me install Firefox

Answer 9

then copy anything you see ...

Answer 10

My mind is blown .... thank you so much.