Q: What is $$\frac{\partial^2}{\partial x_i\partial x_k}\int_{x_i}( a_{ij} (t)x_j + b_i(t))$$
where $a_{ij} =\begin{bmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{bmatrix}$, $\vec{x}= \begin{bmatrix} x_1\\ x_2 \end{bmatrix}$ and $\vec{b}= \begin{bmatrix} b_1\\ b_2 \end{bmatrix}$ , where $a$ and $b$ depend on $t$ ?
Not sure how to approach this expression .. the einstein notation is somewhat confusing