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Partial derivative problem

  1. Feb 9, 2014 #1
    1. The problem statement, all variables and given/known data
    A function f(x,t) depends on position x and time t independent variables. And if [itex]\dot{f}[/itex] represents [itex]\frac{df(x,t)}{dt}[/itex] and [itex]\dot{x}[/itex] represents [itex]\frac{dx}{dt}[/itex], then find the value of [itex]\frac{\partial\dot{f}}{\partial\dot{x}}[/itex].

    2. Relevant equations


    3. The attempt at a solution

    Using the formula for total differential I can have
    [itex]\dot{f}[/itex] = f[itex]_{x}[/itex][itex]\dot{x}[/itex] + f[itex]_{t}[/itex]
    Now when I proceed with differentiating partially the above equation wrt [itex]\dot{x}[/itex] I am struck.
     
  2. jcsd
  3. Feb 9, 2014 #2

    Dick

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    Well, ##f(x,t)## doesn't depend on ##\dot x##, so ##f_x## and ##f_t## don't depend on ##\dot x## either.
     
  4. Feb 9, 2014 #3
    So, I will get the answer as ##f_x##. It's right.

    But I didn't understand why. Can you give me a reference? I would like to read more on this.
     
  5. Feb 9, 2014 #4

    Ray Vickson

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    Why do you say it is right? Is somebody telling you that?
     
  6. Feb 9, 2014 #5

    Dick

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    You could look up Euler-Lagrange equations or Calculus of Variations, but the idea here is to just treat ##x## and ##\dot x## as independent variables.
     
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