With ITO FORMULA and u(t; x) = t we have : d(tBt) = Bt dt

With ITO FORMULA and u(t; x) = w we have : d(tBt) = Bt dt + t dBt.

With ITO FORMULA and u(t; x) = x we have : d(tBt) =  t dBt.

With ITO FORMULA and u(t; x) = tx we have : d(tBt) = Bt dt - t dBt.

With ITO FORMULA and u(t; x) = tx we have : d(tBt) = Bt dt + t dBt.