Differentiating delta function composed with a function

[rms502]

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.

 

[mathman]

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.

 

[lurflurf]

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