Which drug is NOT classified as a narcotic anti-tussive?

Dextromethorphan (Robitussin DM) is the correct answer as it is not classified as a narcotic anti-tussive. Dextromethorphan is a cough suppressant that works on the cough center in the brain, but it does so without the sedative or addictive properties typically associated with narcotics. This makes it a non-narcotic option for treating coughs.

In contrast, codeine phosphate and hydrocodone are both narcotic agents that possess higher potential for dependence and have sedative effects, making them suitable for use in treating severe coughs when non-narcotic options are insufficient. Prednisolone, being a corticosteroid, is utilized for reducing inflammation and is not primarily indicated for treating coughs. Thus, in the context of cough management, dextromethorphan stands out as the non-narcotic anti-tussive.