Given a wave packet:

$\psi({\it x,t}) = \frac{1}{\sqrt{2\pi\hbar}}\int_{-\infty}^{\infty} exp[i(px - \frac{p^{2}}{2m}t)/\hbar]\phi(p){\it dp} $

we are asked to find that $\langle p \rangle$ does not change with time. So it's basically asking us to show $\frac{d}{dt}\langle p\rangle=0$. I know that:

$\frac{d}{dt}\langle p\rangle= -\langle \frac{\partial V}{\partial x}\rangle$

But I'm unsure how to solve for V in this case. Additionally, I've been advised to use the formula:

$\langle p_{x}\rangle = \int \psi^{*}({\bf r},t)(-i\hbar \frac{\partial}{\partial x})\psi ({\bf r},t) d{\bf r}$

and that I will be using a delta function. I'm just kind of lost and trying to figure out which relevant equations to use for this problem and would appreciate some advice on how proceed.