Abstract: The sheaf of logarithmic derivations is an important object to study. In this presentation, I will focus on the question of comparing the Chern class of the logarithmic derivations of a free divisor and the Chern-Schwartz-MacPherson class of the complement of the divisor. When the Jacobian ideal of the free divisor is of linear type, the two classes mentioned above are the same. I will also explain how this result is related to the Logarithmic Comparison Theorem (LCT).