Statistical Mech- basically a differentiation /integral q

[binbagsss]

Homework Statement

See attached.

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.

Homework Equations

see above

The Attempt at a Solution

see above

Many thanks in advance [/B]

 

[Dick]

Homework Statement

See attached.

View attachment 132769

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.

Homework Equations

see above

The Attempt at a Solution

see above

Many thanks in advance [/B]

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