Question

请问这道多元函数求极值的题，求偏导的这一步是怎么得出来的？可以写一下具体过程吗？

Answer 1

①整理可得x-1=(2-z)z'x ③
②整理可得y+1=(2-z)z'y ④
③对x求偏导，1=-z'x*z'x+(2-z)z'xx
z'xx=(1+z'x*z'x)/(2-z)=1/(2-z)
③对y求偏导，0=-z'y*z'x+(2-z)z'xy
z'xy=z'x*z'y/(2-z)=0
同理，④对y求偏导得z'yy=1/(2-z)