I think my teacher was talking about turning y into y(x) or something but I'm just completely lost on this one
Let's do an example to illustrate implicit differentiation:
Now, if you were to ask to find the derivative of this, you could solve for y then differentiate the equation with respect to x. However, not all functions are easily represented only in terms of x (ex. you could not solve for y for this equation: ). Fortunately, we are still able to find the derivative to such functions.
Note that y is a function of x so that we can differentiate it normally. However, we would have to use the chain rule. I think if you study the example, you'll get what I mean:
Looking at the underbrace, notice how we used the power rule (3y^2) and in addition the chain rule (hence the y'). Continuing on to solve for y':
Note it's perfectly fine to have both x and y in our solution to y'.
That is basically the trick when implicitly differentiating equations. See if you can extend this to your question.