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e^(xy)-y = 0, 对x求导， e^(xy)(y+xy')-y' = 0, y' = ye^(xy)/[1-xe^(xy)];
e^z-xz = 0, 对x求导，z'e^z - z - xz' = 0, z' = z/(e^z-x)
u = f(x,y,z)
du/dx = ∂f/∂x + (∂f/∂y)(dy/dx) + (∂f/∂z)(dz/dx)
= ∂f/∂x + {ye^(xy)/[1-xe^(xy)]}(∂f/∂y) + [z/(e^z-x)](∂f/∂z)
e^z-xz = 0, 对x求导，z'e^z - z - xz' = 0, z' = z/(e^z-x)
u = f(x,y,z)
du/dx = ∂f/∂x + (∂f/∂y)(dy/dx) + (∂f/∂z)(dz/dx)
= ∂f/∂x + {ye^(xy)/[1-xe^(xy)]}(∂f/∂y) + [z/(e^z-x)](∂f/∂z)
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