If we have function $y=L(x_1,x_2,x_3,...,x_n)$, and function $z=R(x_1,x_2,x_3,...,x_n)$. How to compute the derivative $\frac{dy}{dz}$?

Shall I do $\frac{dy}{dz} = \sup_{g\in \Re^n}\frac{\bigtriangledown_x L \cdot g}{\bigtriangledown_x R \cdot g}$?

Is there any mathematical term associated with this kind of derivatives?