# Properties of the dirac delta function

1. Jan 7, 2006

### ptabor

I'm trying to show that
$$\int \delta \prime(x-x')f(x') dx = f\prime(x)$$
can I differentiate delta with respect to x' instead (giving me a minus sign), and then integrate by parts and note that the delta function is zero at the boundaries? this will give me an integral involving f' and delta, so the f' would come out - but i'm not sure that this will shift the argument of f to x.
Shankar demonstrates the property on page 62, but I'd like to know if my method is valid.

Last edited: Jan 7, 2006
2. Jan 7, 2006

### dicerandom

Hm, assuming that the integration on the left hand side is actually over $x^\prime$ and that $x$ is within the limits of the integration I belive that you can prove this using integration by parts.

Edit: Sorry, that's what you said

I took a look at Shankar and I like his way better.

Last edited: Jan 7, 2006
3. Jan 7, 2006

### ptabor

yes, his derivation is more tidy and more direct. i did the proof using integration by parts first, and then happened upon his.