小卒資訊論壇 - Powered by Discuz! Board

標題: multivariable function [打印本頁]

作者: peterp2509 時間: 2010-2-27 01:35 PM 標題: multivariable function

consider the function
f(x,y)=x^2tan^-1 (y/x) - y^2tan^-1 (x/y), for xy=/=0,
f(x,y)=0, otherwise

find fx(0,k), fx(0,0), fxy(0,0), fy(h,o), fy(0,0) and fyx(0,0)

please give detail explanation and steps, thx.

作者: hinokari 時間: 2010-2-27 02:12 PM

Check whether i d wrongly

作者: peterp2509 時間: 2010-2-27 02:13 PM 標題: 回覆 #2 hinokari 的帖子

可以就咁D??? 唔知個PARTIAL DERI. 係個POINT EXIST唔EXIST WOR...

作者: hinokari 時間: 2010-2-27 02:39 PM

如果以維基大神來說,http://en.wikipedia.org/wiki/Differentiable
....
partial deri:fx=lim (h->0) f(x+h,y)-f(x,y)/h
計起來好像好麻煩....

作者: peterp2509 時間: 2010-2-27 04:14 PM 標題: 回覆 #5 STEVEGARY 的帖子

可以用L'Hospital Rule??, 點用, 可唔可以講多d

=> fxy(0,0) = 0 (by above Z& trivial)
係咪因為fx(0,0)=0???

作者: peterp2509 時間: 2010-2-27 11:02 PM 標題: 回覆 #7 STEVEGARY 的帖子

但係呢而家係k 變, 咁即係tan^-1 (inf) wor, 咁都用到L'Hospital Rule???

作者: peterp2509 時間: 2010-2-27 11:59 PM

無野，我搞清楚la
問多樣, 點搵derivative of tan^-1 x (forget jor)

作者: hinokari 時間: 2010-2-28 12:08 AM

y=tan-1x
x=tany
dx/dy=sec2y=1+tan2y=1+x2
dy/dx=1/1+x2

歡迎光臨小卒資訊論壇 (http://lsforum.net/board/)