derogate vs underestimate

derogate

verb
  • To act in a manner below oneself; to debase oneself. 

  • To remove a part, to detract from (a quality of excellence, authority etc.). 

  • To take away (something from something else) in a way which leaves it lessened. 

  • To detract from (something); to disparage, belittle. 

underestimate

verb
  • To perceive (someone or something) as having a lower value, quantity, worth, etc., than what he/she/it actually has. 

noun
  • An estimate that is too low. 

How often have the words derogate and underestimate occurred in a corpus of books? (source: Google Ngram Viewer )