设方程 e^z-xyz＝0.确定函数z＝f（x,y）求z对 x的二阶偏导数,怎么求要

f(x,y,z)=e^z-xyz=0
∂z/∂x=-(∂f/∂x)/(∂f/∂z)=-yz/(e^z-xy)=z/[x(z-1)]
∂²z/∂x²=[∂z/∂x x(z-1)-z(z-1+x∂z/∂x)]/[x(z-1)]^2=z/[x(z-1)]x(z-1)-z(z-1+xz/{x(z-1)})]/[x(z-1)]^2
=[z-z^2+z-z^2/(z-1)]/[x(z-1)]^2
=[2z(1-z)-z^2/(z-1)]/[x(z-1)]^2