利用多元函數(shù)的全微分：

z（x，y）=x^y=e^(ylnx);

z(101,99) = (?z/?y)|(x=100,y=100) *△y + (?z/?x)|(x=100,y=100)* △x +z(100,100);

其中，

△y=99-100=-1；

△x=101-100=1;

(?z/?y)|(x=100,y=100)

=lnx*e^(ylnx)|(x=100,y=100)

=100^100*ln100;

(?z/?x)|(x=100,y=100)

=y*x^(y-1)|(x=100,y=100)

=100^100;

(?z/?y)|(x=100,y=100) *△y + (?z/?x)|(x=100,y=100)* △x

=100^100 - 100^100*ln100 <0;

z(100,100)=100^100;

z(101,99) < z(100,100).