...with just accepting that dy/dx is a fraction.
I know I've jeered my physics prof in the past for doing such a thing, but I'm seeing the benefits of his approach. For instance, now it doesn't take any special manipulations to find error, just multiply both sides by dx (or ∂x, depending)!
No more stupid math arguments with my roommate at 1 in morning! It's like I've fully declared my intention to ignore all proper conventions in favour of shortcuts and he gets the smug satisfaction that I'm not doing real math.
Instead I have stupid arguments about American automakers at 1 in the morning. Which ended with an analogy relating GM and Ford to a man getting shot in the head and a man getting shot in the chest, respectively.
Semantics.
They're both screwed.
As an addendum, my roommate is like a puritan when it comes to math. As in accepting nothing other than set theory to be "real" math. That's like saying Ruby isn't real programming because I'm not personally ferrying bits around like a deliveryman.
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