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Differentiating delta function composed with a function

  1. Jun 21, 2013 #1
    Dear all,
    I just wondered whether there was any standard identity to help me solve this equation:
    $$ \int \delta(f(x))^{\prime\prime}g(x) dx $$
    Thanks in advance for your help.
  2. jcsd
  3. Jun 21, 2013 #2


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    Science Advisor

    You don't have an equation.

    I am not sure what you mean by the derivative of the delta function (derivative with respect to what?).

    Integration by parts twice might be an approach.
  4. Jun 21, 2013 #3


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    Homework Helper

    Several things to consider
    \delta(\mathop{f}(x))''=\mathop{f}''(x) \delta (x)+(\mathop{f}'(x))^2 \delta '' (x) \\
    \int \! \delta ^{(n)} (x) \, \mathop{f} (x) \, \mathop{dx}=(-1)^n\int \! \delta (x) \, \mathop{f ^{(n)}} (x) \, \mathop{dx}\\
    \int \! \delta (\mathop{f} (x)) \, \, \mathop{g} (x) \mathop{dx}=\sum_{x \in f^{-1}(0)} \mathop{g}(x)
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