text: """Calculate the partial derivatives of the rate of the dUT1 Earth Orientation Parameter
  
  Description:
  ------------
  
  Calculate the partial derivatives of the rate of the :math:`UT1 - UTC` Earth orientation parameter.
  
  
  \tau = -\hat{K}QRW\vec{b}
  
  
  """
  
  # Midgard imports
  from midgard.dev import plugins
  
  # Where imports
  from where.lib import rotation
  
  
  @plugins.register
  def eop_dut1_rate(dset):
      """Calculate the partial derivative of the rate of the dUT1 Earth Orientation Parameter
  
      Args:
          data:     A Dataset containing model data.
  
      Returns:
          Tuple: Array of partial derivatives, and list of names of derivatives
      """
      column_name = ["ddut1"]
  
      src_dir = dset.src_dir.unit_vector[:, None, :]
      baseline = (dset.site_pos_2.trs.pos - dset.site_pos_1.trs.pos).mat
      dR_dut1 = rotation.dR_dut1(dset.time)
      dt = (dset.time.jd - dset.time.mean.jd)[:, None, None]
      partials = -(src_dir @ rotation.Q(dset.time) @ dR_dut1 @ rotation.W(dset.time) @ baseline @ dt)[:, :, 0]
  
      return partials, column_name, "meter * radians * days / seconds"
  