By analyzing 7.33 fb-1 of e+e- annihilation data collected at center-of-mass energies between 4.128 and 4.226 GeV with the BESIII detector, we report the observation of the semileptonic decay Ds+→η′μ+νμ, with a statistical significance larger than 10σ, and the measurements of the Ds+→ημ+νμ and Ds+→η′μ+νμ decay dynamics for the first time. The branching fractions of Ds+→ημ+νμ and Ds+→η′μ+νμ are determined to be (2.235±0.051stat±0.052syst)% and (0.801±0.055stat±0.028syst)%, respectively, with precision improved by factors of 6.0 and 6.6 compared to the previous best measurements. Combined with the results for the decays Ds+→ηe+νe and Ds+→η′e+νe, the ratios of the decay widths are examined both inclusively and in several ℓ+νℓ four-momentum transfer ranges. No evidence for lepton flavor universality violation is found within the current statistics. The products of the hadronic form factors f+,0η(′)(0) and the c→s Cabibbo-Kobayashi-Maskawa matrix element |Vcs| are determined. The results based on the two-parameter series expansion are f+,0η(0)|Vcs|=0.452±0.010stat±0.007syst and f+,0η′(0)|Vcs|=0.504±0.037stat±0.012syst, which help to constrain present models on f+,0η(′)(0). The forward-backward asymmetries are determined to be (AFBη)=-0.059±0.031stat±0.005syst and (AFBη′)=-0.064±0.079stat±0.006syst for the first time, which are consistent with the theoretical calculation.