Interchangeability of Partial Differentiation in Physics

[mmmboh]

I've tried looking online, but I haven't found the answer. For instance, when can you say (dF_x/dt)=(dF/dt)_x, where subscript x indicates partial differentiation with respect to x.

I know that partial differentiation is pretty much always interchangeable, but what about in this case? I have a physics problem, a Lagrangian, and interchanging how I asked gives the right answer, but I want to make sure it's really legit.

Thanks.

 

[CompuChip]

I suppose that you can always write it out in partial differentiations, e.g.
$$\frac{dF(t, x_1, \ldots, x_n)}{dt} = \frac{\partial F}{\partial t} + \sum_{i = 1}^n \frac{\partial F}{\partial x_i} \frac{\partial x_i}{\partial t}$$
and prove it that way.