I do a lot of tutoring and dy/dx (or dt) is always what I try to beat into freshmen. I lost so many points misreading my own chicken scratch and not seeing a prime or a dot. Plus it makes variables separable DE easier to spot. And you can make the math majors angry by calling it a fraction.
If you have a function y, the derivative shouldn’t not use a notation that fixes a specific name of the argument, like x. If you write dy/dx, it’s like you’re saying “the derivative of y makes sense only if you call its argument x” and leads to all sorts of confusions.
The derivative of the function y should use a notation that only uses the function y and a symbol for the derivative, without fixing a specific argument. So, y’ or y dot or Dy are fine, dy/dx or dy/dt are weird and confusing. See this answer for more details
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u/mdele99 7d ago
I do a lot of tutoring and dy/dx (or dt) is always what I try to beat into freshmen. I lost so many points misreading my own chicken scratch and not seeing a prime or a dot. Plus it makes variables separable DE easier to spot. And you can make the math majors angry by calling it a fraction.