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z=e^-(y/x+x/y)
∂z/∂x
=e^-(y/x+x/y)*(-(y/x+x/y))'
=e^-(y/x+x/y)*(y/x²-1/y)
∂z/∂y
=e^-(y/x+x/y)*(-(y/x+x/y))'
=e^-(y/x+x/y)*(-1/x+x/y²)
所以dz =e^-(y/x+x/y)*(y/x²-1/y)+e^-(y/x+x/y)*(-1/x+x/y²)=e^-(y/x+x/y)*[(y/x²-1/y)+(-1/x+x/y²)]
∂z/∂x
=e^-(y/x+x/y)*(-(y/x+x/y))'
=e^-(y/x+x/y)*(y/x²-1/y)
∂z/∂y
=e^-(y/x+x/y)*(-(y/x+x/y))'
=e^-(y/x+x/y)*(-1/x+x/y²)
所以dz =e^-(y/x+x/y)*(y/x²-1/y)+e^-(y/x+x/y)*(-1/x+x/y²)=e^-(y/x+x/y)*[(y/x²-1/y)+(-1/x+x/y²)]
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