Investigating derivatives by means of combinatorial analysis of the components of the function

• Autores: Moshe Stupel, David Fraivert, Victor Oxman
• Localización: International journal of mathematical education in science and technology, ISSN 0020-739X, Vol. 45, Nº. 6, 2014, págs. 892-904
• Idioma: inglés
• DOI: 10.1080/0020739x.2013.872306
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• Resumen

  • Given a composite function of the form h(x) = f(g(x)), difficulties are often encountered in calculating the value of the nth derivative at some point x= x0when one attempts to determine whether its nth derivative becomes zero at this point, or attempts to find the sign of the nth derivative by differentiating it ntimes and substituting x0.This present paper offers an alternative method that allows the investigation of the nth derivative of function h(x) based on the investigation of functions f?(x) and g(x) only.Several examples are given, which implement the conclusions on the properties of the relation.