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Math Help - Show that (product of these three partial derivatives) = -1.

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    s3a
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    Show that (product of these three partial derivatives) = -1.

    The question is attached along with its solution. This question involves partial differentiation and the implicit function theorem. My work is also attached. I feel that my work is correct but is it incomplete?I have the following questions/confusions.:1) What's the purpose of the solution showing that T=T(P,V) and then F( P,V,T(P,V) )? Couldn't I just as easily have said V=V(P,T) or P=P(V,T) and modified F accordingly?2) Prior to making this forum thread, I was completely confused as to what the 0 = stuff meant before the implication arrow however, I know see that it is the implicit function theorem written in one line. Is this important? Why is it being done in the solution?Any input would be appreciated!Thanks in advance!
    Attached Thumbnails Attached Thumbnails Show that (product of these three partial derivatives) = -1.-question.jpg   Show that (product of these three partial derivatives) = -1.-solution.jpg   Show that (product of these three partial derivatives) = -1.-mywork.jpg  
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