How will the singular values change after right multiplication with the diagonal matrix?

Question

Say that we have an SVD for a matrix $X = U \Sigma V^T$, with the singular values $\sigma_i$. What will happens to the SVD and singular values if we right multiply with a diagonal matrix that simply scales the columns of $X$? Is it possible to write the SVD of $XD$ or get the singular values $\sigma_i$ in terms of the diagonal of $D$ and the SVD of $X$? And more specifically: would it be possible to get the SVD of the $XD$ in terms of the same $U$ we've obtained from the SVD of the X?