So, I understand that implicit differentiation involves derivatives in which x values and y values are mixed up. I've done several implicit differentiation problems a couple sections ago for my math homework, but I pretty just memorized patterns and solved it that way. Now that I'm trying to make sense of related rates, I think it would help to have a better understanding of some of the reasons why its done the way its done. So for example, (d/dx) x2 = 2x. that's pretty understandable. When you take the derivative of y2 its basically done the same way. That's that "pattern memorization" I mentioned. What I don't understand is how they prove this by writing 1. (d/dx) y2 2. (d/dy) (dy/dx) y2 3. (d/dy) y2 (dy/dx) 4. 2y (dy/dx) Understanding that (dy/dx) in step 4 seems to be an important factor in doing related rates, and I seemed to have missed the significance of that. If you want a better reference for what I'm talking about, I'm watching this video on youtube and not understanding the "metamorphosis" to prove the derivative of y2 Edit: So I understand the derivative of any constant times y = ky' So dy/dx is the same as y' which is what I've been using. Maybe when I do related rates I should look at it that way.