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I'm following a statistical mechanics lecture on youtube, and the professor is deriving the average energy as a function of the partition function. He goes:

-1/Z dZ(beta)/d beta = -dlnZ(beta) / d beta

where Z(beta) is the partition function = e^{-(beta) E}.

I spent an hour trying to figure out why the LHS equals the RHS (from both directions, including using differentiation by substitution) but I just can't figure out how he does it.

Perhaps this is a really simple question (and if so, I apologies for my stupidity) but can anyone tell me how to go between the two steps?

Thank you in advance!