I have the following implicit function: $xy=5$.
I want to get $y'$ or $\frac{dy}{dx}$.
In this case, implicit differentiation gives me $\frac{dy}{dx}=\frac{-y}{x}$.
I am curious why explicit differentiation cannot generate the same answer.
That is, $y=\frac{5}{x}$. And then $y'=\frac{dy}{dx} = \frac{-5}{x^2}$.
Any mistake or misunderstanding I have here?