  We derive ages, metallicities, and individual element abundances of early-
and late-type galaxies (ETGs and LTGs) out to 1.5 R$_e$. We study a large
sample of 1900 galaxies spanning $8.6 - 11.3 \log M/M_{\odot}$ in stellar mass,
through key absorption features in stacked spectra from the SDSS-IV/MaNGA
survey. We use mock galaxy spectra with extended star formation histories to
validate our method for LTGs and use corrections to convert the derived ages
into luminosity- and mass-weighted quantities. We find flat age and negative
metallicity gradients for ETGs and negative age and negative metallicity
gradients for LTGs. Age gradients in LTGs steepen with increasing galaxy mass,
from $-0.05\pm0.11~\log$ Gyr/R$_e$ for the lowest mass galaxies to
$-0.82\pm0.08~\log$ Gyr/R$_e$ for the highest mass ones. This strong
gradient-mass relation has a slope of $-0.70\pm0.18$. Comparing local age and
metallicity gradients with the velocity dispersion $\sigma$ within galaxies
against the global relation with $\sigma$ shows that internal processes
regulate metallicity in ETGs but not age, and vice versa for LTGs. We further
find that metallicity gradients with respect to local $\sigma$ show a much
stronger dependence on galaxy mass than radial metallicity gradients. Both
galaxy types display flat [C/Fe] and [Mg/Fe], and negative [Na/Fe] gradients,
whereas only LTGs display gradients in [Ca/Fe] and [Ti/Fe]. ETGs have
increasingly steep [Na/Fe] gradients with local $\sigma$ reaching $6.50\pm0.78$
dex/$\log$ km/s for the highest masses. [Na/Fe] ratios are correlated with
metallicity for both galaxy types across the entire mass range in our sample,
providing support for metallicity dependent supernova yields.
