# Differentiating delta function composed with a function

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.

## Answers and Replies

mathman
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.

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