  We quantify the effect of observational spectroscopic and asteroseismic
uncertainties on regularised least squares (RLS) inversions for the radial
differential rotation of Sun-like and subgiant stars. We first solved the
forward problem to model rotational splittings plus the observed uncertainties
for models of a Sun-like star, HD 52265, and a subgiant star, KIC 7341231. We
randomly perturbed the parameters of the stellar models within the
uncertainties of the spectroscopic and asteroseismic constraints and used these
perturbed stellar models to compute rotational splittings. We experimented with
three rotation profiles: solid body rotation, a step function, and a smooth
rotation profile decreasing with radius. We then solved the inverse problem to
infer the radial differential rotation profile using a RLS inversion and
kernels from the best-fit stellar model.We found that the inversions for
Sun-like stars with solar-like radial differential rotation profiles are
insensitive to the uncertainties in the stellar models. We found that when the
rotation rate below the convection zone is increased to six times that of the
surface rotation rate the inferred rotation profile excluded solid body
rotation. With the current observational uncertainties, we found that
inversions of subgiant stars are sensitive to the uncertainties in the stellar
model. Our findings suggest that inversions for the radial differential
rotation of subgiant stars would benefit from more tightly constrained stellar
models. In Sun-like stars, the insensitivity of the inversions to stellar model
uncertainties suggests that it may be possible to perform ensemble inversions
for the average radial differential rotation of many stars with a range of
stellar types to better constrain the inversions.
