Sir Chad carries a twelve pounder hand cannon, and when he ignites the powder the ball sails true into the main deck of the pirate, but the recoil capsizes his vessel.
Guns have recoil. An equal and opposite reaction to the light bullet going forward really fast is that the heavy gun goes backwards.
The 45-70 round was originally made for rifles, it would take a standing person's entire weight and strength to fight against the force of the bullet going forward.
If you take that same bullet but remove the weight of the rifle, and put it into a little handgun, you will be blown back from the force of the bullet.
So, a derringer is a small pistol, usually with two shots, made for close-range self-defense. Normally they use, well, pistol rounds, like a 9mm, which has like, 700 joules of energy or someshit like that. When you fire a lightweight gun, you definitely get some kickback from it, even with a pistol round.
A 45-70 is a big-ass rifle round with something like 4000 joules of energy behind it. You uh, you put that in a little derringer and pull the trigger, both you and your target are gonna feel it.
A very energetic rifle round (where the mass of the rifle helps control the powerful recoil) being fired from a very low mass handgun would feel quite a bit like holding onto an exploding grenade.