\begin{aligned} \frac{\partial y_{k,l}}{\partial x_{i, j}} &= \sum_{m} \frac{\partial x_{k,m}}{\partial x_{i, j}} W_{m,l}\\ &= \sum_{m} \delta_{i,k} \delta_{m, j} W_{m, j}\\ &= \delta_{i, k} W_{m, l} \end{aligned} \begin{aligned} \left(\frac{\partial L}{\partial \bm{x}} \right)_{i,j} &= \frac{\partial L}{\partial x_{i, j}} \\ &= \sum_{k,l} \frac{\partial y_{k,l}}{\partial x_{i, j}} \frac{\partial