Here's an example of what I mean:

Exercise 1.Findy' ifxy3 +x2y2 + 3x2 - 6 = 1.

Answer.Let us use implicit differentiation. Then we take the derivative of the equation treatingyas a function ofx. We get

Algebraic manipulations give

I don't get where this second y' is coming from. I know the chain rule and product rule and I understand the rules of differenciation, however I suspect my lack of conceptual knowledge impedes me to understand where the y' comes from.

I know the rules of differentiation but I don't know what differentiation is actually doing. It's really come down to a mechanical process.

Please help me understand implict differentiation and what differentiation is doing.

~Kindest Regards

Joey

NOTE> Sorry for double posting