What are the larger types of exoskeletons known as?

Tarantulas do this. Had one in a cage and came on one day to find 2. Turns out it was its exoskeleton after shedding it.

Elizabeth Ann Wesson, I used keep Chilean Rose Haired Tarantulas. They're extremely vulnerable after shedding. However, they need plenty of water before they can shed, otherwise part of their exoskeleton can remain attached to the shedded exoskeleton. If enough water isn't provided, they can lose a limb or more. Remarkably, their limbs can grow back. Spiders are awesome.