9. The Idea of a Derivative of a Function

  1. Ulrich L. Rohde1,2,
  2. G. C. Jain3,
  3. Ajay K. Poddar2 and
  4. A. K. Ghosh4

Published Online: 28 DEC 2011

DOI: 10.1002/9781118130155.ch9

Introduction to Differential Calculus: Systematic Studies with Engineering Applications for Beginners

Introduction to Differential Calculus: Systematic Studies with Engineering Applications for Beginners

How to Cite

Rohde, U. L., Jain, G. C., Poddar, A. K. and Ghosh, A. K. (2011) The Idea of a Derivative of a Function, in Introduction to Differential Calculus: Systematic Studies with Engineering Applications for Beginners, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9781118130155.ch9

Author Information

  1. 1

    BTU Cottbus, Germany

  2. 2

    Synergy Microwave Corporation, Paterson, NJ, USA

  3. 3

    Defense Research & Development Organization, Maharashtra, India

  4. 4

    Department of Aerospace Engineering, Indian Institute of Technology – Kanpur, Kanpur, India

Publication History

  1. Published Online: 28 DEC 2011
  2. Published Print: 9 DEC 2011

ISBN Information

Print ISBN: 9781118117750

Online ISBN: 9781118130155

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Keywords:

  • idea of derivative of a function;
  • instantaneous velocity, problem and instantaneous speed;
  • differentiability of a function, continuity of that function

Summary

This chapter contains sections titled:

  • Introduction

  • Definition of the Derivative as a Rate Function

  • Instantaneous Rate of Change of y [=f(x)] at x = x1 and the Slope of its Graph at x = x1

  • A Notation for Increment(s)

  • The Problem of Instantaneous Velocity

  • Derivative of Simple Algebraic Functions

  • Derivatives of Trigonometric Functions

  • Derivatives of Exponential and Logarithmic Functions

  • Differentiability and Continuity

  • Physical Meaning of Derivative

  • Some Interesting Observations

  • Historical Notes