I've fired a derringer once -- a copy of the old Remington double barrel (don't know what make) in .38 sp. It was during a CAS match. I found it hard to handle, hard to shoot accurately (even at spitting distance) and with a truly lousy trigger.
As a novelty to play with at the range -- maybe. As a serous working gun -- why? Some of the small .380 and even 9x19 auto-loaders are almost as small but much more useful.
"It is long been a principle of ours that one is no more armed because he has possession of a firearm than he is a musician because he owns a piano. There is no point in having a gun if you are not capable of using it skillfully." -- Jeff Cooper