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This is indeed a bug! Thanks for reporting it! What version of Sage were you using?
I can reproduce the bug in Sage 7.4 using PowerSeriesRing instead of PowerSeries:
sage: R.<x> = PowerSeriesRing(SR)
sage: f = 1 + O(x^2)
sage: f.derivative()
O(x^1)
sage: g = O(x^0)
sage: g.derivative()
O(x^-1)
