This is an announcement for the paper "Differentiability of Banach spaces via constructible sets" by Hadi Haghshenas. Abstract: the main goal of this paper is to prove that any Banach space X , that every dual ball in X** is weak* separable, or every weak* closed convex subset in X**is weak* separable , or every norm-closed convex set in X* is constructible, admits an equivalent Frechet differentiable norm. Archive classification: math.FA Mathematics Subject Classification: 46B20 Remarks: 5 pages The source file(s), DIFFERENTIABILITYOFBANACHSPACESVIACONSTRUCTIBLESETS.tex: 12164 bytes, is(are) stored in gzipped form as 0810.0586.gz with size 5kb. The corresponding postcript file has gzipped size 43kb. Submitted from: h_haghshenas60@yahoo.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0810.0586 or http://arXiv.org/abs/0810.0586 or by email in unzipped form by transmitting an empty message with subject line uget 0810.0586 or in gzipped form by using subject line get 0810.0586 to: math@arXiv.org.