Let $\Omega_X^1(\log D)$ be the (locally free) of logarithmic differentials on a smooth projective variety $X$ with respect to a simple normal crossing divisor $D$.

What are the Chern classes of $\Omega_X^1(\log D)$ in terms of the Chern classes of $\Omega_X^1$ and $D$? I think, the first one is $$c_1(\Omega_X^1(\log D))= c_1(\Omega_X^1)+D.$$