When y can't be isolated without turning one equation into multiple equations, you can just take the derivative of both sides, using all the rules (Chain Rule, Product Rule, Quotient Rule, etc), without worrying about isolating y, and then isolate y'.
It will generally be easier to isolate y' than y when implicit differentiation is necessary because y prime always appears in the numerator, and to the first power.
The cases when implicit differentiation is necessary are generally when y is put to some power other than 1, and especially (not exclusively!) when it is locked inside a root after being added to something else.
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