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Statistical Mech- basically a differentiation /integral q

  1. Apr 8, 2017 #1
    1. The problem statement, all variables and given/known data

    See attached.

    period.png

    to get ##p## I need to differentiate ##F## w.r.t ##V##, but I also have that the upper limit ##T_{D}## depends on ##V##, so I must take this into consideration when doing the differentiation.

    The solution looks as though it has done this without evaluating the integral, so rather it has differentiated the integral as usual and then added a term which is evaluated at the upper limit ##\frac{T_D}{T}## and then multiplied by ##\frac{\partial}{\partial } (\frac{T}{T_D})##

    So this is clearly some sort of product rule, but can somebody just explain the second term more formally to me, it isn't inegrated wr.t. ##x## so I think some sort of chain rule is at work with the ##\frac{\partial}{\partial V}## but I can't seem to get it.
    2. Relevant equations

    see above
    3. The attempt at a solution

    see above

    Many thanks in advance
     
  2. jcsd
  3. Apr 8, 2017 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    It's just this https://en.wikipedia.org/wiki/Leibniz_integral_rule, isn't it?
     
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