Question

apply the chain rule for implicit differentiation to find $\frac{partial z}{partial w}$. $\frac{partial z}{partial w}=-\frac{f_{w}}{f_{z}}$

Explanation:

Step1: Recall implicit - differentiation formula

For an implicit function $F(w,z) = 0$, by the chain - rule for implicit differentiation, the formula for $\frac{\partial w}{\partial z}=-\frac{F_z}{F_w}$, where $F_z=\frac{\partial F}{\partial z}$ and $F_w=\frac{\partial F}{\partial w}$.

Answer:

$-\frac{F_z}{F_w}$