calculus and analysis - Derivative after numerical Integration

So I have a function that I want to numerically integrate with respect to temperature, so the integral changes depending on the value of temperature being used as it is one of the bounds.

After integrating I want to be able to take the derivative with respect to temperature and plot it. I must just be messing up the code on the second part though.

numericalModelInternalEnergy[Td_, T_] := 
 Alpha*T^4*NIntegrate[x^3/(Exp[x] - 1), {x, 0, Td/T}] + ground

Alpha and ground are just constants and this gives a function that when I specify Td (a parameter) and the temperature it returns the value. So I can do a plot like this:

Plot[numericalModelInternalEnergy[670, T], {T, 0, 1000}]

Now I just want to get the derivative of the above function with respect to T, which I thought would just be the following, but it doesn't seem to work with the plotting.

numericalModelHeatCapacity[Td_, T_] := 
 Derivative[0, 1][numericalModelInternalEnergy][Td, T]

Comments

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