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 don't 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 don't want to simply copy it because 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?