The recent advent of hard x-ray free electron lasers (XFELs) opens new areas of science due to their exceptional brightness, coherence, and time structure. In principle, such sources enable studies of dynamics of condensed matter systems over times ranging from femtoseconds to seconds. However, the studies of "slow" dynamics in polymeric materials still remain in question due to the characteristics of the XFEL beam and concerns about sample damage. Here we demonstrate the feasibility of measuring the relaxation dynamics of gold nanoparticles suspended in polymer melts using X-ray photon correlation spectroscopy (XPCS), while also monitoring eventual X-ray induced damage. In spite of inherently large pulse-to-pulse intensity and position variations of the XFEL beam, measurements can be realized at slow time scales. The X-ray induced damage and heating are less than initially expected for soft matter materials.