One of the reasons that the Fourier transform is so useful is that it converts operations on function f in to different operations on the function ˆ f . In this paper we discuss some properties of differentiability of Fourier transform and we generalize the results that are stated by many other authors, and we give some propriety in Schwartz's space S using the main result. Mathematics Subject Classification. 43A15, 43A32, 43A62.