The eternal battle between mathematicians and physicists continues! While mathematicians clutch their pearls over mathematical purity, physicists are out here treating derivatives like fractions and canceling them willy-nilly! The horror!
In the rigorous world of math, d/dx is a differential operator that follows specific rules. But walk into a physics classroom and you'll see d's flying around, getting canceled, and multiplied like they're having a wild party!
Non-standard analysis? Who has time for that when there's a universe to figure out? Physicists be like: "Does it work? Great! Moving on to the next unsolved mystery of the cosmos!"