A simple functional derivative

[sprik]

Hi!
I am doing some numerical calculations recently. I need to calculate the functional derivative. eg. functional :
$$n(\rho)=\int dr'r'\rho(r')f(r,r')$$
it need to calculate:
$$\frac{\delta n(r)}{\delta\rho(r')}$$

I think the derivative is r'f(r,r'). Is this right?

Thanks very much!

 

[Dyson]

I calculate it like this:
$$\frac{\delta n(r)}{\delta \rho(r^{\prime \prime})}=\int dr^{\prime} r^{\prime}\delta (r^{\prime}-r^{\prime \prime })f(r, r^{\prime})=r^{\prime \prime}f(r,r^{\prime \prime})$$
So, I think your result is right.