So I remember in Calculus I they told me that (d/dx)f(x) is just a short-hand for lim_(x-->a)... etc. Then they pulled a fast one that I didn't notice at the time, and has annoyed me ever since. They split off the dx and used it in integrals, and never explained how this was valid. In general I don't get the validity of reasoning with an infinitesimal like d. Is there anywhere I can read about this? I took a course in introductory Analysis and still don't feel comfortable with it.