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A fundamental problem in differential privacy is to release privatized answers to a class of linear queries with small error. This problem has been well studied in the static case. In this paper, we consider the fully dynamic setting where items may be inserted into or deleted from the dataset over time, and we need to continually release query answers at every time instance. We present efficient black-box constructions of such dynamic differentially private mechanisms from static ones with only a polylogarithmic degradation in the utility.