How to calculate and store (ArcMap) slope on huge mosaic dataset?

I have a huge raster dataset stored in a geoDB (DHM with 2m resolution for all of Switzerland), uncompressed size ~75 GB. I want to use the ArcMap Slope tool (or another tool would also work) to calculate slopes for the whole country.

How do I go about processing such a huge dataset?

Is it possible to process this "tile by tile" (since it is already mosaiced, there should be some tiling?). Also unclear to me: The result will be of similar size… what would be an efficient way to store the result? I don’t have write access on the DB it is coming from, but I could create a new DB.