In implicit differentiation, we find ∂ z ∂ x {\displaystyle \displaystyle {\frac {\partial z}{\partial x}}} by − F x F z {\displaystyle \displaystyle -{\frac {F_{x}}{F_{z}}}}
Hence ∂ z ∂ x = − y z + 1 x y + 3 z 2 {\displaystyle \displaystyle {\frac {\partial z}{\partial x}}=-{\frac {yz+1}{xy+3z^{2}}}}
by 
