  The higher Nash blowup of an algebraic variety replaces singular points with
limits of certain spaces carrying higher-order data associated to the variety
at non-singular points. In this note we will define a higher-order Jacobian
matrix that will allow us to make explicit computations concerning the higher
Nash blowup of hypersurfaces. Firstly, we will generalize a known method to
compute the fiber of this modification. Secondly, we will give an explicit
description of the ideal whose blowup gives the higher Nash blowup. As a
consequence, we will deduce a higher-order version of Nobile's theorem for
normal hypersurfaces.
