Final answer:
Antonin Dvořák's music was first promoted by Johannes Brahms, leading to international recognition and increased demand for his compositions.
Step-by-step explanation:
Antonin Dvořák's music was first promoted by Johannes Brahms, who was one of the leading musicians of the time. After meeting Dvořák, Brahms was impressed with his music and recommended the young Czech composer to his own publisher, Fritz Simrock. This proved to be a pivotal moment in Dvořák's career as it led to a significant increase in the demand for his compositions, with his music gaining international recognition.