In multi-variable calculus, if I write $f(x,y,z)$, it is assumed that $x,y,z$ are independent.
I'd like to model a quantity $F$, that is a function of 3 related quantities, $x,y,z$. In fact, $xy=z$. I thought about writing $F$ as $F(x,y,z)$, but this would be incorrect; in particular, $\frac{\partial F}{\partial x}$ would be meaningless because when $y$ and $z$ are held constant, $x$ is constant as well.
What is the best way to model or express $F$ mathematically?