I have an easy question which I've been thinking about for a while.. Lets say I want to take the derivative of a function y = f(x) with respect to x, we would get. dy/dx = f'(x). In the couple of books I've skimmed through, they all say that dy/dx is not a ratio but the notation that implied taking the derivative of y with respect to x. Question: If dy/dx is not a ratio then how come the differential of y is equal to f'(x)dx? It almost seems as they are multiplying both sides by dx. This can't be mathematically correct, can it? I would like to know mathematically how dy is equal to f'(x)dx.