derogatory vs in bad

derogatory

• Disparaging. 

• Tending to derogate 

• Reducing the power or value of (a governmental body, etc); detracting from. 

• Lessening the worth of (a person, etc); expressing derogation; insulting. 

• Being or pertaining to a derogatory clause. 

• A trade-line on a credit report that includes negative credit history. 

in bad

• (Canada, US, informal) in bad odour with someone, out of favour with someone, in someone's bad books