Kempf-Laksov formula expresses every Schubert class of the Grassmannian as a determinant of a matrix whose entries are Chern classes. The formula is generalized to K-theory by Hudson-Ikeda-M.-Naruse in 2015. In this talk, I will explain a further generalization of this determinant formula to the infinitesimal cohomology theory, which is a simplest example of oriented cohomology theories beyond Chow ring and K-theory. The talk is based on a joint work with Thomas Hudson.