Green’s Dictionary of Slang

1. the head [? the Derby hat, which sits on the SE head].

1927		Chi. Dly News 2 Aug. f.n. 2 in Illinois Association for Criminal Justice et al. Illinois Crime Survey (1929) 862: It is their [i.e. two police sergeants] assignment to humor and protect any City Hall politician who might get unruly in the place, but to bounce a black-jack on the derby of any stranger who might complain about the service .
1930		E.H. Lavine Third Degree (1931) 109: Two billiard cues bounced on his derby, shoulders and body.
1967		(con. 1950s) McAleer & Dickson Unit Pride (1981) 328: You don’t think I’d sit by doin’ nothin’ while Billy gets his derby kicked in?

2. (US black) an act of oral sex [? the Derby hat, which sits on the SE head/head n. (2c); ? the bobbing/jolting action of a jockey on horseback].

1969		‘Iceberg Slim’ Pimp 172: If she ain’t too shy to show what her ‘Derby’s’ like.
1972		R.A. Wilson Playboy’s Book of Forbidden Words.
1984		L. Paros Erotic Tongue n.p.: The professionals helped forge a common tongue. A man now had his joint copped, had some derby, or had his hat nailed to the ceiling. More frequently, men spoke of being blown or having a blow job (all since early 20th C).

3. see darby n.¹