Hey Doc, I helped a guy with the same situation years ago out in Seattle. He would work on jobs and quite for the day by noon because all his batteries were dead. There are two problems here:
First, if you're charging something like a Dewalt drill battery, it probably has a regular household AC cord from the charger base that plugs into the wall. Those type chargers are very sensitive to AC sine waves. I plugged one into a Vector model 750 watt inverter that was hooked to a 12 volt battery once, it burned the charger up in less than a minute. For that type of charger you need either regular utility power, a gas fired generator, or a sine wave inverter. The wave forms from those sources are perfectly rounded. Sive wave inverters are generally quite expensive, a 110 volt output model rated at maybe 100 watts will cost you a few hundred dollars, and there are not very many of them around. Most sine wave inverters are in the several thousand watt size for running households and RV's. You can get a modified sine wave inverter very inexpensively at an auto parts store, truck stop, or even Home Depot. A 750 watt model like ours will cost around $70 USD. Ours runs our 110 volt weed whip and any of my AC drills.
If you have a tool with a smaller battery, and it charges with a wall pack transformer that has a skinny cord that plugs into the tool, or its battery, it will work fine on the cheaper modified sine wave inverters. Wall pack transformers have isolation type transformers installed in them prior to the voltage regulation, so the choppy sine wave of the cheaper inverters is smoothed out before it gets to the sensitive electronics. The DeWalt type charger bases don't do this. Almost any size will work, most battery chargers of this type use less than 25 to 50 watts of AC power, so a 750 watt inverter could run a power strip full of them simultaneously.
The other problem was mentioned by your previous answerer. If you take a good size inverter, like our 750 and hook it to your truck battery without the engine on, in an hour, you might not get it to start. Running the motor all that time opens up other problems as well though. What we did in Seattle was this. We bought two Trojan T-105 golf cart batteries. They are 6 volts each, so if you wire them together in series you get 12 volts. Then we grounded the negative side of the new pack, and ran a heavy wire through a driving lamp relay ($5.95 at auto parts store) to the positive of the regular truck battery. Now when he drives, he turns on the switch on the dash that activates the relay, and the golf cart batteries charge while he's driving. When he gets to the site, he turns off the motor and the switch, the battery banks separate, and the golf cart batteries run his inverter for several hours or longer. Even if the golf cart batteries run down, the motor will still start with the regular truck battery. Makes for great camping too, and backup power for your home from your truck. The batteries probably cost about $90 each today, and the inverter another $75. Just remember you can't run those DeWalt type chargers on that $70 inverter. What is really nice about that truck setup is that with that inverter and two golf cart batteries, he can actually run an extension cord from his truck to his 110 volt drill, and not bother with the rechargeables. Or he can run the 110 volt drill, but charge other items with wall pack transformers at the same time. Golf cart batteries hold 220 amp hours each, probably more than twice any 12 volt battery you'll find on the shelf, and they really hold up well to repeated charges and discharges. We actually run our entire home on them each night with a 4000 watt sine wave inverter, my batteries are almost 10 years old now. Just keep them watered regularly. Good luck Doc, and take care, Rudydoo