beginning vs derivative

beginning

noun
  • That which begins or originates something; the source or first cause. 

  • The act of doing that which begins anything; commencement of an action, state, or space of time; entrance into being or upon a course; the first act, effort, or state of a succession of acts or states. 

  • The initial portion of some extended thing. 

  • That which is begun; a rudiment or element. 

adj
  • Of or relating to the first portion of some extended thing. 

derivative

noun
  • Something derived. 

  • A financial instrument whose value depends on the valuation of an underlying asset; such as a warrant, an option etc. 

  • A word that derives from another one. 

  • The value of such a derived function for a given value of its independent variable: the rate of change of a function at a point in its domain. 

  • The linear operator that maps functions to their derived functions, usually written D; the simplest differential operator. 

  • Any of several related generalizations of the derivative: the directional derivative, partial derivative, Fréchet derivative, functional derivative, etc. 

  • A chemical derived from another. 

  • The derived function of f(x): the function giving the instantaneous rate of change of f; equivalently, the function giving the slope of the line tangent to the graph of f. Written f'(x) or (df)/(dx) in Leibniz's notation, ̇f(x) in Newton's notation (the latter used particularly when the independent variable is time). 

adj
  • Having a value that depends on an underlying asset of variable value. 

  • Lacking originality. 

  • Imitative of the work of someone else. 

  • Obtained by derivation; not radical, original, or fundamental. 

  • Referring to a work, such as a translation or adaptation, based on another work that may be subject to copyright restrictions. 

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