OrePolynomial[{{-2*t^2 + 121*t^4 + 475*t^6 - 1746*t^8 + 1152*t^10, {3}}, 
  {-2*t + 665*t^3 + 201*t^5 - 7506*t^7 + 5760*t^9, {2}}, 
  {2 + 519*t^2 - 1929*t^4 - 5310*t^6 + 3456*t^8, {1}}}, 
 OreAlgebraObject[{Der[t]}, Together, Together[#1 + #2] & , 
  Together[#1*#2] & , None], DegreeLexicographic]
