Partial derivative that contains the independent variable as an deriva

[merrypark3]

Homework Statement

$\frac{\partial f}{\partial t},\frac{\partial f}{\partial x}$ where $f=f(x,t,\frac{dx}{dt})$

Homework Equations

The Attempt at a Solution

I think it's impossible to consider it as a simple partial derivative.

 

[haruspex]

No, it's quite valid. E.g. suppose f represents a force which can act on a particle and depends on the position pf the particle, its speed, and time. A different trajectory of the particle could lead to its having the same speed at the same time, but be in a slightly different position. The affect on f would depend on the partial derivative wrt x.