= Solution
{c}
With $q=p'-p$ and the routing just described, multiplication of the three <QED Feynman rules> for the <Feynman vertices>, the two <Dirac propagators> and the <photon propagator> gives $(-ie_D)^3i^2(-i)=-e_D^3$. Hence the unrenormalized amputated <Feynman vertex> through this order is
$$
\boxed{iV^\mu(p,p')=-ie_D\gamma^\mu-e_D^3\int\frac{d^Dk}{(2\pi)^D}\frac{\gamma^\nu(\not p'-\not k+m)\gamma^\mu(\not p-\not k+m)\gamma_\nu}{(k^2+i0)[(p'-k)^2-m^2+i0][(p-k)^2-m^2+i0]}+O(e_D^5).}
$$
For the renormalized <Feynman vertex>, add $-ie_D\delta_1\gamma^\mu$ to this expression. Contributions from replacing parameters inside the one-loop term by their bare counterparts enter at higher <loop order>.
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