# Partial derivative that contains the independent variable as an deriva

1. Oct 9, 2013

### merrypark3

1. The problem statement, all variables and given/known data

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

2. Relevant equations

3. The attempt at a solution

I think it's impossible to consider it as a simple partial derivative.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Oct 9, 2013

### 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.