The question is, why implicit differentiation applies to equations [ Because they're not functions ]
As we know, we can apply derivation to the functions, and I know that in implicit differentiation we consider $y$ as a function of $x$, but what that function is?
I had also asked another question which didn't get a satisfying answer for it, it is also related to this matter.
Please, please, please to infinity , don't give Wikipedia link of the theorems.I just wonder about those people who copy/paste the Wikipedia links, if Wikipedia was satisfying, I would have never asked my questions in here.
I will absolutely appreciate whoever gives enlightening piece of favor!
*As a side note, people around me, students, and TA's can't even understand the question.So, it has become really important for me to know the answer!