Integral definition of the logarithmic function and the derivative of the exponential function in calculus

• Autores: Alexander Vaninsky
• Localización: International journal of mathematical education in science and technology, ISSN 0020-739X, Vol. 46, Nº. 3, 2015, págs. 450-456
• Idioma: inglés
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• Resumen

  • Defining the logarithmic function as a definite integral with a variable upper limit, an approach used by some popular calculus textbooks, is problematic. We discuss the disadvantages of such a definition and provide a way to fix the problem. We also consider a definition-based, rigorous derivation of the derivative of the exponential function that is easier, more intuitive, and complies with the standard definitions of the number e, the logarithmic, and the exponential functions.