Which of the following drugs can cause skin discoloration if used on the face?

Silver sulfadiazine is the correct answer because it is a topical antimicrobial commonly used in the treatment of burn wounds and other skin infections. One of the notable side effects of silver sulfadiazine is that it can cause a temporary gray or bluish discoloration of the skin, particularly when applied to areas with high circulation or those that are frequently exposed to sunlight. This discoloration results from silver ions being deposited in the skin, which can be more pronounced on the face due to its thin skin and exposure.

In contrast, rifampin, while it can cause discoloration, primarily affects bodily fluids such as urine and saliva rather than the skin. Sulfasalazine can cause skin reactions, but it is not commonly associated with discoloration of the skin when applied topically. Trimethoprim-sulfamethoxazole also does not lead to skin discoloration as a typical side effect; rather, it may cause other dermatological reactions. Thus, silver sulfadiazine stands out as the agent specifically known for inducing skin discoloration at the application site.