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We study $D_{s}^{+}$ decays to final states involving the $\eta'$ with a482$\,$pb$^{-1}$ data sample collected at $\sqrt{s}$ = 4.009$\,$GeV with the\mbox{BESIII} detector at the BEPCII collider. We measure the branchingfractions $\mathcal{B}(D^+_{s}\rightarrow \eta'X)$ = (8.8$\pm$1.8$\pm$0.5)$\%$and $\mathcal{B}(D_{s}^{+}\rightarrow \eta'\rho^{+})$ = ($5.8\pm1.4\pm0.4$)$\%$where the first uncertainty is statistical and the second is systematic. Inaddition, we estimate an upper limit on the non-resonant branching ratio$\mathcal{B}(D_{s}^{+}\rightarrow \eta'\pi^+\pi^0)<5.1\%$ at the 90$\%$confidence level. Our results are consistent with CLEO's recent measurementsand help to resolve the disagreement between the theoretical prediction andCLEO's previous measurement of $\mathcal{B}(D_{s}^{+}\rightarrow\eta'\rho^{+})$.

Measurement of the branching fractions of $D_{s}^{+}\rightarrow \eta'X$ and $D_{s}^{+}\rightarrow \eta'\rho^{+}$ in $e^+e^-\to D^+_{s}D^-_{s}$