How do you unclog a bathtub?

Yeah, any of the commercial drain cleaners are safe. Usually a plunger will do the job, though. Just don't plunge while there is drain cleaner in the water. The spatter can blind you.

If there is ever a problem in the commode, you have to read the instructions. Some cleaners are not safe there.

once the clog is removed, get one of these --

That is what I use in my bathtubs and they have never clogged up. Uh, does that say "Pet" on it? I haven't seen that before. In the grocery store they are with the utensils, not in the pet section.

works on all types of mammalian hair...

Use two plungers -- use one to seal over the overflow drain, the other to plunge the floor drain. No point pouring chemicals down the drain if you can loosen a big clog the old fashioned way.

If you live in an old house, it's possible that the weight of the tub has caused the floor around it to settle, as well as the pipes that take water away. This can progress to the point where water flowing out has to flow uphill for a few feet. This will cause the tub to empty slowly, and will also greatly increase the rate at which stuff accumulates in the pipe...

duct tape can also be used to seal the overflow...

What is there that that stuff can't do, eh?

Hey, I like that. No way I could handle two plungers at once.