How to find y', when xy=1 .

So I was doing step iii, 2000, Q1; and I needed to differentiate xy=1, and I didn't use implicit differentiation which I think gave me the wrong answer. Which makes me wonder which is ALWAYS the better way to differentiate? I'm starting to think implicit may be the way to go, because you get the derivative at every point (like in circles) and also you don't need to solve for y algebraically.

So which one is it? $y'=-x^{-2}$ or $y'=x/y$?

y = x^-¹
y' = -1/x²

xy = 1
d/dx : y + x y' = 0
y' = - y/x
y' = - 1/x²

Same thing

It changes on situation, for that, was easier to Re arrange to for y and differentiate.

In a circle for example, probably best to go implicitly

I know but it took me about 15 min to think about doing it implicitly, which would have been disastrous in the real exam. My question is which is ALWAYS better? I'm talking here about when the coordinates themselves are unknown btw.

There's never an always... That defeats the whole point of step, you adapt to a situation