We don't recommend using synthetic fertilizers for several reasons
1) They are water soluble and therefore:
a) The plant has no way to control how much fertilzer it
b) Most of the fertilizer is washed away in rains
2) Also, when the ferilizer is washed away it accumulates in the local water table and leads to eutrophication which, leads to the death of phyto and zooplankton in waterways.
and there are other reasons which are escaping me that the moment.
Anyway, what I recommend is to spread some well composted manure in the area. This fall, spread some mulched up leaves over the area and cover that with some manure. Next year, your potatoes will go nuts.
For now, the manure will give your potatoes a good go. Another thing that you can spread in the area is Kelp Meal. It is a slow release organic fertilizer that will provide the plants with both Macro (NPK) and micro nutrients.