Using the chain rule again shows that D(\mathbf{x}\circ\mathbf{C}) = \mathbf{x}_r r' + \mathbf{x}_{\theta}\theta' + \mathbf{x}_{\phi}\phi'. All dot products \mathbf{x}_i \cdot \mathbf{x}_j where i and j differ are zero, so the squared norm of this vector is
