Question

apply the chain rule for implicit differentiation to find $\frac{partial w}{partial x}$. $\frac{partial w}{partial x}=-\frac{f_x}{f_w}$

Explanation:

Step1: Recall implicit - differentiation chain - rule formula

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

Answer:

$-\frac{F_x}{F_w}$