Let z = Z (x, y) be an implicit function determined by the equation f (x-z, Y-Z), where f (U, V) has a continuous partial derivative of the first order

z(x)+z(y)=-(f(x)+f(y))/f(z)
f(x)=f1(1-z(x)-f2z(x))
f(y)=-f1z(y)+f2(1-z(y))
f(z)=-f1-f2
So Z (x) + Z (y) = 1 + Z (x) + Z (y)
So Z (x) + Z (y) = 0.5
Note: bracketed is its partial derivative, and F1F2 is also its derivative

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