  We describe a procedure for extracting momentum derivatives of nucleon matrix
elements on the lattice directly at $Q^2=0$. This is based on the Rome method
for computing momentum derivatives of quark propagators. We apply this
procedure to extract the nucleon isovector magnetic moment and charge radius as
well as the isovector induced pseudoscalar form factor at $Q^2=0$ and the axial
radius. For comparison, we also determine these quantities with the traditional
approach of computing the corresponding form factors, i.e. $G^v_E(Q^2)$ and
$G_M^v(Q^2)$ for the case of the vector current and $G_P^v(Q^2)$ and
$G_A^v(Q^2)$ for the axial current, at multiple $Q^2$ values followed by
$z$-expansion fits. We perform our calculations at the physical pion mass using
a 2HEX-smeared Wilson-clover action. To control the effects of excited-state
contamination, the calculations were done at three source-sink separations and
the summation method was used. The derivative method produces results
consistent with those from the traditional approach but with larger statistical
uncertainties especially for the isovector charge and axial radii.
