设z=z(x,y)æ¯ç±æ¹ç¨z=y+lnï¼x/zï¼ç¡®å®çéå½æ°ï¼æ±åzåxï¼å¯¹æ±åºæ¥çåzåxååy
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解ï¼F(x,y,z)=z-y+lnx-lnzâ¡0............(1)
ӘF/Әx+(ӘF/Әz)(Әz/Әx)=1/x+(1-1/z)(Әz/Әx)=0,æ
Әz/Әx=z/[x(1-z)],
Ә²z/ӘxӘy=[x(1-z)(Әz/Әy)+xz(Әz/Әy)]/[x(1-z)]²={[x(1-z)+xz]/[x(1-z)]²}(Әz/Әy)
=[1/x(1-z)²](Әz/Әy).........................(2)
ä¸é¢æ±Әz/Әy:ç±æçå¼(1)å¾ï¼
ӘF/Әy+(ӘF/Әz)(Әz/Әy)=Әz/Әy-1-(Әz/Әy)/z=(Әz/Әy)(1-z)-1=0,
æ
Әz/Әy=1/(1-z)ï¼ä»£å
¥(2)å¼å¾ï¼
Ә²z/ӘxӘy=1/x(1-z)³
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