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Derivative of O(x^0)

Consider a power series

R.<x> = PowerSeries(SR)
f = 1 + O(x^2)
f.derivative()

This gives us O(x^1) as we would expect. However, if we do

f = O(x^0)
f.derivative()

we get O(x^-1) instead of O(x^0) again. Is this a bug or am I missing something?

Derivative of O(x^0)

Consider a power series

R.<x> = PowerSeries(SR)
f = 1 + O(x^2)
f.derivative()

This gives us O(x^1) as we would expect. However, if we do

f = O(x^0)
f.derivative()

we get O(x^-1) instead of O(x^0) again. Is this a bug or am I missing something?