These both pertain to flight planning and are mainly a function performed by dispatch.
Derived alternate minimums are a method to standardize, and in most cases override, the minimum weather required, on an airport-by-airport basis, for filing such an airport as an alternate on a flight plan. If you go to AirNav and search for really any public airport, you'll usually see a chart at the bottom with the title NOTE: Special Alternate Minimums Apply. Under Part 121 OpsSpecs, we are allowed to override those and use a standard formula to determine what the minimums need to be at our alternate airports to list them on a flight plan. The formula is based on the number of navaids and types of approaches at the airport.
During an actual flight, this becomes irrelevant. If you have to divert, you can legally commence an approach at any suitable airport that is at or above the published minimums for the chosen instrument approach.
Exemption 17347 is invoked on a fairly regular basis where I fly, especially this time of the year (autumn). Essentially, so long as certain conditions are met, you can be legally dispatched to an airport more than 60 minutes away (including taxi time) if the airport's TAF indicates weather will be lower than the minimums you need to commence an approach. There are a host of exceptions and requirements within the rule, but if you can conceptualize what I just wrote, you'll be off to a goods start. When we apply this, we have the OpsSpec open on our tablet. It's not something one can easily commit to memory.