This guy is your stereotypical bully. While he doesn't actually appear in the book except in Stanley's recollections of his life before Camp Green Lake, his relationship with Stanley gives us some inside info about Stanley's personality.
Derrick is smaller than Stanley, but he still manages to push Stanley around. The school's teachers even find it amusing that "a little kid like Derrick could pick on someone as big as Stanley" (6.22). This is one of the first clues we get that Stanley isn't the type to stand up for himself – he's more of a "lie down and take it" kind of kid.