By far the hardest thing for me was notation for partial derivatives. Having never been shown just how to actually interpret the symbols, I had great difficulty parsing what was actually meant by various expressions.
Eventually, I abandoned the more common notations entirely, and fell back on other notation we had been shown, like $f_1(x,y,x)$, which means "the derivative of $f$ in the first argument, evaluated at $(x,y,x)$".
These days, I have a deeper understanding of just what my problem was. Roughly speaking, $dx$ makes sense on its own, but $\partial/\partial x$ does not; the latter depends not on $x$, but on a curve $x$ is being viewed as a parameter for. (e.g. it suffices to view $x$ as a component in a coordinate system)