In single variable calculus, there is only one independent variable. Calculus courses normally use $f'(x)$ to denote “the derivative” of $f(x)$, and rarely emphasize that this is “the derivative with respect to $x$”. Leibniz notation is not emphasized.

Similarly, there are mathematicians who regard (single) integration to be fundamentally about antidifferentiation. These mathematicians — and some calculus texts — regard the “$dx$” in an integral as superfluous, and therefore write “$\int f(x)$” for “the integral” of $f(x)$.

This makes the transition to multivariable calculus quite difficult for many students. Even if they have seen Leibniz notation, they are typically quite uncomfortable working with infinitesimals — differentiation and integration are taught as procedures to memorize, rather than as operations involving ratios or sums of small quantities. And the essential step of asking “with respect to what” has not yet become a habit.