Suppose $z = x + y$ and in addition, there is a function $f(z)=F(x,y)$ for all values. Is there a way to relate,
$\frac{df}{dz}, \frac{\partial F}{\partial x}\text{ and }\frac{\partial F}{\partial y}\textrm{?}$
In general, suppose $z = g(x,y)$, what is the relationship (if any)?