Derivative of the partition function Help

vuser88

i need to show that the average value of the energy is -(1/Z)(dZ/dBeta)= -(d/dBeta)Ln(Z)

where Z is the partition function i know how to do the first part, i dont know how to show this is equal to the derivative w/ respect to beta of lnZ. i think my math is wrong when taking Ln(Z)

Beta = 1/kT
Z= sum over s of { e^ (beta*E(s)) }
any suggestions,

ps i do have the solution from cramster but i dont want to simply copy it cuz then i will never learn anything

vuser88

im pretty sure sure this is the chain rule, but it dosent work out when i actually do it step by step

Bill_K

Are you aware that the derivative of ln(Z) is 1/Z?