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Derivative of the Dirac Delta

  1. Sep 1, 2008 #1
    Derivative Using Dirac Delta Function

    1. The problem statement, all variables and given/known data
    Let [tex]\theta[/tex](x) be the step function:

    [tex]\theta[/tex](x) be equivalent to

    1, if x > 0
    0, if x [tex]\leq[/tex] 0

    Show that [tex]\frac{d \theta }{dx}[/tex] = [tex]\delta[/tex](x)


    2. Relevant equations
    In the previous portion I was able to prove
    x [tex]\frac{d}{dx}[/tex] ([tex]\delta[/tex](x))= -[tex]\delta[/tex](x)


    3. The attempt at a solution
    I thought the problem was a heavyside problem but upon closer inspection, I noticed that on the heavyside step function it is 1 when x [tex]\geq[/tex] 0.

    So how do I resolve this? Is there a way to change it so that it looks like a heavyside function, because that makes the problem much more convenient.:rofl:
     
  2. jcsd
  3. Sep 2, 2008 #2

    tiny-tim

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    Science Advisor
    Homework Helper

    Hi CasualDays! :smile:

    (have a theta: θ and a delta: δ :smile:)

    Hint: what is 1 - θ(x)? :wink:
     
  4. Sep 2, 2008 #3
    It's always the easy solutions that allude me..:biggrin:
     
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