Usually in class there are examples when you are able to find these derivatives by derivativating both sides and at the end you can simply cross out some parts and get y' simply by dividing.
In this example I can't figure out what to do next:
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I don't ask to do all the work, leave some for me too :)
This is as far as I got, maybe I made a mistake so now can't see anything to divide.
Found one mistake, but doesn't change much, not (x+y)^2 but (x-y)^2