code: def _compute_dk_dtau_on_partition(self, tau, p):
          
          y, r2l2 = self._compute_y(tau, return_r2l2=True)
          # Compute the d^(|pi|)f/dy term:
          dk_dtau = self._compute_dk_dy(y, len(p))
          # Multiply in each of the block terms:
          for b in p:
              dk_dtau *= self._compute_dy_dtau(tau, b, r2l2)
          return dk_dtau
docs: Evaluate the term inside the sum of Faa di Bruno's formula for the given partition.
          
          Parameters
          ----------
          tau : :py:class:`Matrix`, (`M`, `D`)
              `M` inputs with dimension `D`.
          p : list of :py:class:`Array`
              Each element is a block of the partition representing the
              derivative orders to use.
          
          Returns
          -------
          dk_dtau : :py:class:`Array`, (`M`,)
              The specified derivatives over the given partition at the specified
              locations.