I'm reading up on some of the history behind leibniz derivative notation, which had more human elements to it than I expected.
From what I gather, Leibniz had a way of thinking about derivatives that involved quotients, which is why it looks like division. But then people said division isn't precise enough, don't do that. But, since it was already being used everywhere, they kept using the notation, even though it looks exactly like a fraction. My guess is that the 'd' stands for 'delta' (triangle), which comes from the original notation. I wonder what caused that change. I'd be very amused if it came down to something like "d is easier to write".