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Derivative of a special function

  1. Aug 25, 2010 #1
    Let f(x) be the following function:

    f(x)=[tex]\infty[/tex],if x<0 or x>a;f(x)=0,if 0<x<a.

    What’s the derivative of f(x) at x=0 and x=a? I know that the derivative of step function is [tex]\delta[/tex](x) , but what will occur if the jump is infinite?
     
  2. jcsd
  3. Aug 25, 2010 #2
    f ' (x) = dx*f(x)
     
  4. Aug 25, 2010 #3

    mathman

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    In general the derivative of a jump of size a at u is aδ(x-u). your a is -∞ and u=0.
     
  5. Aug 29, 2010 #4
    Thanks for your reply.
     
  6. Aug 29, 2010 #5

    HallsofIvy

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    Note that the "function" you give is not really a function. And Jjaquelin and mathman had to use "generalized functions" to give an answer.
     
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