[xvedejas]

Is `dy/dx` ever distinct from `d/dx y`? Generally I've treated `df(x)/dx` as just another way to write the operator `d/dx` applied to `f(x)`, which I don't think of as a fraction.

[lupire]

dy/dt = dy/dx * dx/dt

[xvedejas]

That's just the chain rule, right?

d/dt y(t) = ( d/dx y(x) )( d/dt x(t) )