Usage of the word derogatory

HI,
can anyone tell me where to use the word?..I know it means offensive…But little comfused about the usage…

Use it in more formal language.

Here are some examples from Time magazine:

70 1960-04-04 , " A Good English Teacher " March 14, an implication derogatory to English teachers in general. It is that English teachers
71 1961-04-07 We are astonished at the fertile imagination of your writers in finding derogatory adjectives which, in addition to being inaccurate, seem to
72 1962-06-01 Odessa. His paper broke out in a rash of loud headlinesNOTHING DEROGATORY ABOUT GRAIN STORAGE, and POLITICAL HACKS KEEP UP STRUGGLES FOR
73 1962-06-01 Odessa. His paper broke out in a rash of loud headlinesNOTHING DEROGATORY ABOUT GRAIN STORAGE, and POLITICAL HACKS KEEP UP STRUGGLES FOR
74 1963-02-22 supplement. This flashy bit of New World journalism had drawn only derogatory cracks and a small hello when Thomson introduced it last year
75 1963-12-20 " When the U.S. officially protested these words, Cambodia denied any derogatory intentions toward President Kennedy, but it huffily recalled its ambassador
76 1963-12-20 " When the U.S. officially protested these words, Cambodia denied any derogatory intentions toward President Kennedy, but it huffily recalled its ambassador
77 1965-01-29 fine-combing their collections for all sorts of song titles that might sound derogatory, such as I Kiss Your Hand, Madame, The
78 1965-03-12 as Attorney General he had tried to plant in LIFE magazine a derogatory story about Teamster President Jimmy Hoffa at a time when Hoffa
79 1965-04-23 inning, the Dodgers were ahead 2-0, and the blossomed with derogatory signs. PHOOEY! said one. Said another: WAIT
80 1965-11-12 ; 3) had " not read, seen or heard anything derogatory about the party, " and 4) would not doubt
81 1965-11-28 's Republican Senator Hugh Scott moved to strike from the report any derogatory mention of Williams. The Democratic majority, permitting neither discussion
82 1966-01-08 , a cheat and a lover of " black necks " a derogatory Kikuyu reference to the darker-skinned Luo. Moreover, suggested Jomo
83 1966-11-20 ’ to any group or individual or engage in the use of derogatory terms such as nigger, boy, spic, wop,
84 1969-04-25 ‘s dervish foreign policy has earned him the almost automatic and somewhat derogatory appellation " mercurial. " Yet Sihanouk maintains that there is
85 1970-03-09 PIG. The term is not used, however, in a derogatory sense since the three letters point up the motto awarded them
86 1970-08-03 insists that his watches are " in no way meant to be derogatory. " He does admit that " hidden political comment "
87 1970-11-18 Khrushchev and dismissed by conservative critics as a " formalist " a derogatory term for a Soviet writer who allows himself to become preoccupied
88 1971-02-15 has collected 10,000 fan letters v. seven in a file marked " derogatory. " Paul Harvey, the conservative commentator, has dispatched
89 1971-12-27 . " The rebuff has not stopped Karras from having the last derogatory word. As quick with a quip as he once was
90 1971-12-27 from the press box. " He’s done nothing but say derogatory things about the team, " said Lion Public Relations Director
91 1971-12-27 I must assume the reason for his column is to say more derogatory things. " The rebuff has not stopped Karras from having
92 1972-02-21 the standards of the time, the play was considered risque and derogatory to Irish society; the controversy escalated to street riots.
93 1973-08-27 and complex " ways, he would " ask the FBI for derogatory information of one type or another on Senators in his own
94 1974-03-22 plumbers’ operation. Ehrlichman told Colson of a project to get derogatory information about Ellsberg. Colson would then have to devise a
95 1974-06-17 : plastic surgery Tip: to leave Yam: a black (derogatory) Zex: careful, someone’s coming Many of those
96 1974-11-04 Conn. Nelson A. Rockefeller apologizing to Arthur J. Goldberg about that derogatory book was similar to a professional boxer beating up an ordinary
97 1974-11-25 of them public officials, and that he had secretly authorized a derogatory book about his Democratic opponent, Arthur J. Goldberg, in
98 1975-01-13 to obstruction of justice for devising a scheme to get and disseminate derogatory information about Pentagon Papers Defendant Daniel Ellsberg in 1971; serving
99 1975-03-31 Bravo! A cover story that will probably cause a rash of derogatory letters from jealous housewives and the fans of Lawrence Welk,
100 1975-09-01 to, married, husband, wife… and other derogatory terms. " More seriously, the couple agreed to allow