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We gave a simple derivation of density operator with the quantum analysis. Wedealt with the functional of a density operator, and applied maximum entropyprinciple. We obtained easily the density operators for the Tsallis entropy andR\'enyi entropy with the $q$-expectation value (escort average), and alsoobtained easily the density operators for the Boltzmann-Gibbs entropy and theBurg entropy with the conventional expectation value. The quantum analysisworks effectively in the calculation of the variation of the functional whichincludes trace.

Derivation of density operators for generalized entropies with quantum analysis