"they derived great comfort from this assurance"

• base a concept on an extension or modification of (another concept)

  "some maintain that he derived the idea of civil disobedience from Thoreau"

• (of a word) have (a specified word, usually of another language) as a root or origin

  "the word ‘punch’ derives from the Hindustani ‘pancha’"

• arise from or originate in (a specified source)

  "words whose spelling derives from Dr Johnson's incorrect etymology"

• (of a sentence in a natural language) be linked by a set of stages to (its underlying logical form)
• (of a substance) be formed or prepared by (a chemical or physical process affecting another substance)

  "strong acids are derived from the combustion of fossil fuels"

• obtain (a function or equation) from another by a sequence of logical steps, for example by differentiation

  "the volume fraction of the soil can then be derived as a function of L"