  We gave a simple derivation of density operator with the quantum analysis. We
dealt with the functional of a density operator, and applied maximum entropy
principle. We obtained easily the density operators for the Tsallis entropy and
R\'enyi entropy with the $q$-expectation value (escort average), and also
obtained easily the density operators for the Boltzmann-Gibbs entropy and the
Burg entropy with the conventional expectation value. The quantum analysis
works effectively in the calculation of the variation of the functional which
includes trace.
