Partial derivative that contains the independent variable as an deriva

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Homework Statement



[itex]\frac{\partial f}{\partial t},\frac{\partial f}{\partial x}[/itex] where [itex] f=f(x,t,\frac{dx}{dt})[/itex]

Homework Equations





The Attempt at a Solution



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

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
haruspex
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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.
 

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