Calculating the derivative of piecewise functions

B. Tomas Johansson*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Exercises involving the calculation of the derivative of piecewise defined functions are common in calculus, with the aim of consolidating beginners’ knowledge of applying the definition of the derivative. In such exercises, the piecewise function is commonly made up of two smooth pieces joined together at one point. A strategy which avoids using the definition of the derivative is to find the derivative function of each smooth piece and check whether these functions agree at the chosen point. Showing that this strategy works together with investigating discontinuities of the derivative is usually beyond a calculus course. However, we shall show that elementary arguments can be used to clarify the calculation and behaviour of the derivative for piecewise functions.

Original languageEnglish
Pages (from-to)144-148
JournalInternational Journal of Mathematical Education in Science and Technology
Issue number1
Early online date28 May 2015
Publication statusPublished - 2016


  • Darboux's theorem
  • derivative
  • differentiable function
  • mean-value theorem
  • piecewise function


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