>>12798355Of course yours is true because it's a simple substitution.
What I meant was (dx/dt)^2 != d^2x/dt^2
Or higher dimensions when you have
u(x1,x2,x3) -> du = du/dx1 dx1 + du/dx2 dx2 + du/dx3 dx3
Or partial derivatives.
It's not that the abuse of notation isn't useful, it's that I hated it when my profs said "you'll learn it later" or "don't let the mathematicians see this" and we didn't learn it later and the mathematicians stayed far away from the physics lectures.
