  We present new measurements of the evolution of the galaxy stellar mass
functions (GSMF) and UV luminosity functions (UV LF) for galaxies from $z=6-9$
within the Frontier Field cluster MACSJ0416.1-2403 and its parallel field. To
obtain these results, we derive the stellar masses of our sample by fitting
synthetic stellar population models to their observed spectral energy
distribution with the inclusion of nebular emission lines. This is the deepest
and farthest in distance mass function measured to date and probes down to a
level of M$_{*} = 10^{6.8}M_{\odot}$. The main result of this study is that the
low-mass end of our GSMF to these limits and redshifts appears to become
steeper from $-1.98_{-0.07}^{+0.07}$ at $z=6$ to $-2.38_{-0.88}^{+0.72}$ at
$z=9$, steeper than previously observed mass functions at slightly lower
redshifts, and we find no evidence of turnover in the mass range probed. We
furthermore demonstrate that the UV LF for these system also appears to show a
steepening at the highest redshifts, without any evidence of turnover in the
luminosity range probed. Our $M_{\mathrm{UV}}-M_{*}$ relation exhibit shallower
slopes than previously observed and are in accordance with a constant
mass-to-light ratio. Integrating our GSMF, we find that the stellar mass
density increases by a factor of $\sim15_{-6}^{+21}$ from $z=9$ to $z=6$. We
estimate the dust-corrected star formation rates (SFRs) to calculate the
specific star formation rates ($\mathrm{sSFR}=\mathrm{SFR/M_{*}}$) of our
sample, and find that for a fixed stellar mass of $5\times10^{9}M_{\odot}$,
sSFR $\propto(1+z)^{2.01\pm0.16}$. Finally, from our new measurements, we
estimate the UV luminosity density ($\rho_{\textrm{UV}}$) and find that our
results support a smooth decline of $\rho_{\textrm{UV}}$ towards high
redshifts.
