To adjust to sudden shifts in conditions, microbes possess regulated genetic mechanisms that sense environmental challenges and induce the appropriate responses. The initial evolution of microbes in new environments is thought to be driven by regulatory mutations, but it is not clear how this evolution is affected by how quickly conditions change (i.e. dynamics). Here, we perform experimental evolution on continuous cultures of tetracycline resistant E. coli in different dynamical regimens of drug administration. We find that cultures evolved under gradually increasing drug concentrations acquire fine- tuning mutations adapting an alternative efflux pump to tetracycline. However, cultures that are instead periodically exposed to large drug doses evolve transposon insertions resulting in loss of regulation of the main mechanism of tetracycline resistance. A mathematical model shows that sudden drug exposures overwhelm regulated responses, which cannot induce resistance fast enough. These results help explain the frequent loss of regulation of resistance in clinical pathogens.