Here's an example of what I mean:
Exercise 1. Find y' if xy3 + x2y2 + 3x2 - 6 = 1.
Answer. Let us use implicit differentiation. Then we take the derivative of the equation treating y as a function of x. 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.
NOTE> Sorry for double posting