Explanation:

- The phrase "a medical specialist who administers drugs for relieving pain during surgery" refers to a healthcare professional focused on pain management in surgical settings.

- Dermatologist (Option 1): A dermatologist is a doctor specializing in skin, hair, and nail conditions. They are not involved in administering pain relief during surgery.

- Anesthetist (Option 2): An anesthetist is a medical specialist who administers anesthesia to relieve pain during surgery, making them the correct match for the described role.

- Nephrologist (Option 3): A nephrologist is a doctor specializing in kidney care and treating kidney-related diseases, unrelated to pain management during surgery.

- Analgesic (Option 4): An analgesic is a type of medication used to relieve pain, not a specialist.