The entire first semester of my Calculus class we used Lagrange's notation, f'(x), f''(x), etc.. So at the beginning of second semester the teacher kinda casually switched over to Leibniz notation, dy/dx, which left all of the class dazed. I understood it pretty well until she did a simple problem, dy/dx=2x/y. She asked us to find the anti-derivative of it so I cross multiplied. (dx)(2x)=(dy)(y). The way I understand it is that dx or dy is an infinitesimal change in x or y. So an infinitesimal change in x times 2x would approach 0 and an infinitesimal change in y times y would approach 0 too. Then I can't take the anti-derivative. I need a better explanation of this because obviously I'm doing something wrong. Any help is welcomed thanks.