Implicit differentiation is really the chain rule in disguise. All the y's on both sides of the equation can be very confusing. The trick is to realize that those y's are functions of x, we just don't know what those functions are. we will apply the chain rule, and treat y as the "inside function." The trick to understanding implicit differentiation is realizing that we are applying the chain rule to a function y that we don't know. So the derivative of y we just call y'.
