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Does this notation for partial derivatives work?

  1. Oct 28, 2009 #1
    I noticed that for partial calculus equations I can use Jacobians
    \left(\frac{\partial A}{\partial B}\right)_C=\frac{\partial(A,C)}{\partial(A,B)}
    You immediately get the triple product rule
    and of course the other rule

    Now I was surprised to see that even the pseudo-equation for the chain rule
    works well even if I treat all terms as a real variable.

    My question is: Does this algebra for partial derivatives always work despite crazy manipulations and cancellations?
  2. jcsd
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