Moved from a technical forum, so homework template missing

The dipole potential is given by:

##\displaystyle\psi=\int_{V'} \dfrac{\rho}{|\mathbf{r}-\mathbf{r'}|} dV'

+\oint_{S'} \dfrac{\sigma}{|\mathbf{r}-\mathbf{r'}|} dS'##

I need to prove that ##\psi## is differentiable at points except at boundary ##S'## (where it is discontinuous)

I know if partial derivatives of ##\psi## "exist and are continuous" everywhere except at boundary ##S'##, then ##\psi## is differentiable everywhere except at boundary ##S'##.

How shall I proceed in showing partial derivatives of ##\psi## exist?

Thanks for any help in advance.

##\displaystyle\psi=\int_{V'} \dfrac{\rho}{|\mathbf{r}-\mathbf{r'}|} dV'

+\oint_{S'} \dfrac{\sigma}{|\mathbf{r}-\mathbf{r'}|} dS'##

I need to prove that ##\psi## is differentiable at points except at boundary ##S'## (where it is discontinuous)

I know if partial derivatives of ##\psi## "exist and are continuous" everywhere except at boundary ##S'##, then ##\psi## is differentiable everywhere except at boundary ##S'##.

How shall I proceed in showing partial derivatives of ##\psi## exist?

Thanks for any help in advance.