Question

apply the chain rule for implicit differentiation to find ∂w/∂y. ∂w/∂y = - f_w/f_y

Explanation:

Step1: Recall implicit - differentiation formula

For an implicit function $F(w,y) = 0$, the formula for $\frac{\partial w}{\partial y}$ using the chain - rule is $\frac{\partial w}{\partial y}=-\frac{F_y}{F_w}$, where $F_y=\frac{\partial F}{\partial y}$ and $F_w=\frac{\partial F}{\partial w}$.

Answer:

$-\frac{F_y}{F_w}$