First of all, I notice that most of these words are Latin-derived or French-derived, except for
belittle. Whether a word is of Anglo-Saxon or Latin origin often determines its register (the level of formality it is associated with). Latin = more formal; Anglo-Saxon = less formal. The context in which they are used is also important. In everyday conversation, you can use the first four almost interchangeably, but if you were using them in writing, you might want to consider their etymology and context.
All quotes below are from the Online Etymology Dictionary.
late 14c., "degrade socially" (for marrying below rank or without
proper ceremony), from Anglo-French and Old French desparagier (Modern
French déparager) "reduce in rank, degrade, devalue, depreciate,"
originally "to marry unequally, marry to one of inferior condition or
rank," and thus, by extension, to bring on oneself or one's family the
disgrace or dishonor involved in this, from des- "away" (see dis-) +
parage "rank, lineage" (see peer (n.)).
Also from late 14c. as "injure or dishonor by a comparison,"
especially by treating as equal or inferior to what is of less
dignity, importance, or value. Sense of "belittle, undervalue,
criticize or censure unjustly" is by 1530s. Related: Disparaged;
1781, "to make small, reduce in proportion," from be- + little (v.);
first recorded in writings of Thomas Jefferson (and probably coined by
him), Jefferson used it in "Notes on the State of Virginia" to
characterize the view promoted as scientific by French naturalist
Georges-Louis Leclerc Buffon that American species (including humans)
were naturally smaller than and inferior to European ones, which
Jefferson was at pains to refute. ("So far the Count de Buffon has
carried this new theory of the tendency of nature to belittle her
productions on this side of the Atlantic.")
1520s, "to sully or stain" (the reputation, character, etc.), from
Latin denigratus, past participle of denigrare "to blacken; to
defame," from de- "completely"
This word is used in HTML to refer to an element which will be discontinued in the next version.
1620s, "to pray against or for deliverance from, pray the removal or
deliverance from," from Latin deprecatus, past participle of deprecari
"to pray (something) away," from de "away" (see de-) + precari "to
pray" (from PIE root *prek- "to ask, entreat"). Meaning "to express
disapproval, urge against" is from 1640s.
This word is used in accounting to describe the expected decrease in value of an item over the years.
mid-15c., "to undervalue, under-rate," from Latin depretiatus, past
participle of depretiare "to lower the price of, undervalue," from de
"down" (see de-) + pretium "price" (see price (n.)). From 1640s in
transitive sense of "lessen the value of, to lower in value."
Intransitive sense of "to fall in value, become of less worth" is from
So actually they all mean something different and are used in different contexts.
Deprecate and depreciate are two different concepts and are not synonymous.