I don't know about the person you're responding to, but those operations over what usually appears at the denominator of the derivative purely for notation purpose has always looked to me as complete magical garbage. What object is "dx" ? is it a number ? a limit ? is it zero ? can i divide another number by it ?
I think this notation is single handly the reason why i've never been comfortable with calculus.
PS: i've stumbled a few years ago on a math book that described the original concept of "infinitesimals" and how a whole different way of doing calculus exists. And it seems to me those kinds of computations over "dx" come from there. But the end result of mixing concepts really looks like trash.
I think this notation is single handly the reason why i've never been comfortable with calculus.
PS: i've stumbled a few years ago on a math book that described the original concept of "infinitesimals" and how a whole different way of doing calculus exists. And it seems to me those kinds of computations over "dx" come from there. But the end result of mixing concepts really looks like trash.