reserve L for Abelian left_zeroed add-associative associative right_zeroed
              right_complementable distributive non empty doubleLoopStr;
reserve a,b,c for Element of L;
reserve R for non degenerated comRing;
reserve n,m,i,j,k for Nat;
 reserve D for Function of R, R;
 reserve x,y,z for Element of R;
reserve D for Derivation of R;
reserve s for FinSequence of the carrier of R;
reserve h for Function of R,R;
 reserve R for domRing;
 reserve f,g for Element of the carrier of Polynom-Ring R;
reserve a for Element of R;

theorem Th36:
    (Der1(R)).(f*g) = ((Der1(R)).f)*g + f*((Der1(R)).g)
    proof
      per cases;
        suppose f is non constant;
         hence thesis by Th35;
        end;
        suppose f is constant;
          hence thesis by Th34;
        end;
      end;
