MOST derringers, and other miniature firearms are intended to be used in a two handed shooting stance- one hand holds the firearm, the other hand holds the shoulder of your opponent..... (GRIN) Seriously, not just the short barrel, but rudimentary sights, very short sight radius, trigger pull usually really bad, questionable grip- reason these are usually known as "belly guns". OTH, have a 2" S&W Mdl 36 that will shoot a decent shot group at 50 ft. But that ain't a derringer.
Over the years I've owned derringers in various styles and calibers. I think I've always had one. Many are cheaply made and inaccurate. Last year I bought a Cobra .22 magnum derringer. It is, beyond any doubt, the nicest shooting and most accurate derringer I've ever owned. Bar none!
I've owned .38 caliber derringers, and found them to have very sharp and painful recoil. I finally had to buy a pair of padded gloves to shoot it. It wasn't much fun.
I like derringers and enjoy shooting them, but I would NEVERrecommend them as a primary self defense arm. Backup and recreational shooting, you betcha. Because of their very short barrels, you won't get much accuracy beyond 10 feet or so, but that's what they are designed for, up close and personal.
A Ruger LCP is cheaper, lighter, and not much bigger. It also fits in a pocket nicely I totally understand if you want a derringer as a novelty, but as a serious defensive firearm it comes up a little short.