Final answer:
The postganglionic neurotransmitter of the sweat glands in the sympathetic nervous system is acetylcholine (ACh), which binds to muscarinic receptors.
Step-by-step explanation:
In the sympathetic nervous system, an exception to the common neurotransmitter release pattern is observed with the postganglionic fibers that innervate sweat glands. Instead of releasing norepinephrine, these sympathetic fibers release acetylcholine (ACh) which then binds to muscarinic receptors on the sweat glands. This creates a physiological response resulting in the production and secretion of sweat. It's important to note that the glands respond to ACh even though they are part of the sympathetic system, which typically uses norepinephrine for its neurotransmission with other targets.