$\frac{\partial \mathbf{x}\mathbf{x}^{T}}{\partial \mathbf{x}}$ is this calculatable? I know $\frac{\partial \mathbf{x}^{T}\mathbf{x}}{\partial \mathbf{x}} = \mathbf{x}$, but what is the
$\frac{\partial \mathbf{x}\mathbf{x}^{T}}{\partial \mathbf{x}}$?
Is this calculatable? If it is, can anyone tell me how to derivative it? Thank you so much

Well to me the operator
$$
\frac{\partial}{\partial \textbf{x}}=\sum_{j=1}^{N}\hat{e}_j\frac{\partial}{\partial x_j}
$$
$$
\textbf{x}\textbf{x}^{T}=\sum_{m,n}\hat{e}_m\hat{e}_n x_m x_n
$$
$$
\frac{\partial}{\partial\textbf{x}}\textbf{x}\textbf{x}^{T}=\sum_{j,m,n}\hat{e}_j\hat{e}_m\hat{e}_n(x_n\frac{\partial x_m}{\partial x_j}+x_m\frac{\partial x_n}{\partial x_j})=
\sum_{j,m,n}\hat{e}_j\hat{e}_m\hat{e}_n(x_n\delta_{j,m}+x_m\delta_{j,n})=\sum_{m,n}(\hat{e}_m\hat{e}_m\hat{e}_n x_n+\hat{e}_n\hat{e}_m\hat{e}_n x_m)
$$
The object appears to be a rank three tensor. 
