Mathematics

This is implicit differentiation—you're finding the slope of a circle without solving for $y$ explicitly. The key insight is to differentiate both sides with respect to $x$, treating $y$ as a function of $x$ and applying the chain rule to any term containing $y$. Then rearrange to isolate $\frac{dy}{dx}$.

This is implicit differentiation—you're finding the slope of a circle without solving for $y$ explicitly. The key insight is to differentiate both sides with respect to $x$, treating $y$ as a function of $x$ and applying the chain rule to any term containing $y$. Then rearrange to isolate $\frac{dy}{dx}$.