Implicit Differentiation using given point

I have an issue with implicit differentiation. It's probably because I don't really understand the chain rule? So I'm posting a question here and hoping for an explanation. As in, I want to know when I should do the derivative, where dy/dx should be multiplied, things like that and why. From what I've seen online, people do this differently and it just confuses me so a standard process I can follow every time would be helpful.

x^3+y^3=4xy+1, (2,1)

I'm not sure if I should move 4xy to the left or just keep it on the right? And then an explanation for the rest would be greatly appreciated. Thanks so muchh.

Post Merge: 11 years ago

And another equation: x cos y = 1, (2, pi/3). So hopefully the process that was used in the first problem can be figured out to use for this problem too. Again, thanks so much.