# derivatives of ln of summation

by mmwave
Tags: derivatives, summation
 P: 211 Summations and calculus gives me fits so please verify my results on these 2 issues: 1. Z = summation ( exp ( - B*E(s)) ) where the sum is over s d/dB of ln(Z) = d/dB (ln (exp(-BEo) + exp(-BE1) + ... exp(-BEn)) = (exp(-BEo) + exp(-BE1) + ... exp(-BEn))^-1 + (-E0*exp(-BEo) + -E1*exp(-BE1) + ... -En*exp(-BEn)) = summation ( E(s) * exp(-B*E(s)) / summation ( exp(-B*E(s)) which is also the average value of E when Prob(E(si)) = exp(-BE(si)) 2. does d/dT of exp( -E/kT) = -E/k * exp(-E/kT) * -(1/T^2) = E/k* 1/T^2 * exp(-E/kT) ? If you're curious, these come up in Boltzmann statistics in thermal physics.
 P: 837 Looks fine to me.
 P: 2 Hi, where did the last term come from in 2nd question? Also i want to ask what is d/d(ni)[summation(ni*ln(ni))]? i:from 1 to r. ni is n sub indice i

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