(Semi-)leptonic D$_{(s)}$ decays at BESIII

BESIII has collected $2.93$ and $6.32\,\mathrm{fb^{-1}}$ of e$^+$e$^-$ collision data samples at $3.773$ and $4.178$-$4.226$ GeV, respectively. We will report precision measurements of $f_{D_{(s)}}$, $|V_{cs}|$, and test of lepton flavor universality by studying the leptonic decays of $D_s^+ \rightarrow l \nu$ with $\tau^+ \rightarrow \rho^+ \nu$, $\pi^+ \nu$, and $e^+ \nu \nu$. We will also report the observation of semileptonic decay of $D^0 \rightarrow \rho^-\mu^+\nu$ and lepton flavor universality test, and the studies of some other semileptonic decays, such as $D_s^+ \rightarrow \pi^0\pi^0e^+\nu$ and $D_s^+ \rightarrow K_s^0 K_s^0 e^+\nu$.