Malliavin's derivative operator is an exceedingly useful tool in probability theory, stochastic analysis, and applications. We will show how boundedness conditions on this operator can be used to extend random field regularity results beyond the sub-Gaussian case. We will also show that one can define the Ito integral and prove the Ito formula for arbitrary Gaussian processes (including all fractional Brownian motions) via an extended Skorohod theory based on Malliavin derivatives.