Mathematics

This problem asks you to find the rate of change of $x$ with respect to $y$ — which is the reciprocal perspective on implicit differentiation. Instead of the usual $\frac{dy}{dx}$, you're treating $y$ as the independent variable. Differentiate both sides with respect to $y$ (remembering that $x$ is now the dependent variable), apply the product and chain rules carefully, then solve for $\frac{dx}{dy}$ algebraically.

This problem asks you to find the rate of change of $x$ with respect to $y$ — which is the reciprocal perspective on implicit differentiation. Instead of the usual $\frac{dy}{dx}$, you're treating $y$ as the independent variable. Differentiate both sides with respect to $y$ (remembering that $x$ is now the dependent variable), apply the product and chain rules carefully, then solve for $\frac{dx}{dy}$ algebraically.