  Using 482~pb$^{-1}$ of $e^+e^-$ collision data collected at a center-of-mass
energy of $\sqrt{s} = 4.009$ GeV with the BESIII detector, we measure the
branching fractions of the decays $D_s^+\to\mu^+\nu_\mu$ and
$D_s^+\to\tau^+\nu_\tau$. By constraining the ratio of decay rates of $D_s^+$
to $\tau^+\nu_\tau$ and to $\mu^+\nu_\mu$ to the Standard Model prediction, the
branching fractions are determined to be $\mathcal{B}(D_s^+ \to \mu^+\nu_\mu) =
(0.495 \pm 0.067 \pm 0.026)\%$ and $\mathcal{B}(D_s^+ \to \tau^+\nu_\tau) =
(4.83 \pm 0.65 \pm 0.26)\%$. Using these branching fractions, we obtain a value
for the decay constant $f_{D_s^+}$ of $(241.0 \pm 16.3 \pm 6.5)~\text{MeV}$,
where the first error is statistical and the second systematic.
