HighlightsOn the Jacobians of the Factors of the Truncated Singular Value DecompositionThe aim of this paper is to derive analytical expressions for the Jacobians for the factors of the Truncated Singular Value Decomposition (TSVD) of a matrix. The starting point of this study is an earlier work by \cite{GratTshi16} on the second-order expansion of the truncated singular subspace decomposition. We consider the first-order Fréchet derivatives expressions found in that work to establish the Jacobians. We then specialize the found results to singular vectors and singular values. We show that our results are consistent with earlier works on particular cases. A numerical example is performed to confirm the validity of our theory.