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B Inverse of a differential?

  1. Dec 3, 2016 #1
    Hello everybody,
    If I define [tex] z_\mu = \frac{\partial{\phi}}{\partial{x^{\mu}}}, \, \mu = 0,1,...,n [/tex], (for some scalar function phi of x=(x_0,...,x_n)) how is then [tex] \frac{\partial{}}{\partial{z_{\mu}}} [/tex] defined or rather what is it equal to? How would you call this expression? the inverse of a differential?

    Thank you.
  2. jcsd
  3. Dec 3, 2016 #2


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    Science Advisor

    It is not an inverse of anything. It is a partial derivative.
  4. Dec 4, 2016 #3
    What is it equal to or how can i calculate it please?
  5. Dec 4, 2016 #4

    Stephen Tashi

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    Science Advisor

    The expression is a differential operator. Unless you state a specific function of ##z_\mu## for it to operate upon, there is nothing to calculate.
  6. Dec 4, 2016 #5


    Staff: Mentor

    As already explained, it's an operator. By itself, without a function for it to operate on, it has no meaning. Your question is similar to "What is ##\sqrt{}## equal to?
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