In the sequence problem we saw the equation of loss with respect to weight as \frac{\partial L_{t}(\theta)}{\partial W} = \frac{\partial L_{t}(\theta)}{\partial s_{t}} \sum_{k =1}^{t}\prod_{j = k}^{t  1}\frac{\partial s_{j+1}}{\partial s_{j}}\frac{\partial s_{k}}{\partial W}. Here, what would be the result of \frac{\partial s_{k}}{\partial W}?

{\partial s_{k}} is a vector then what will be the partial derivative of a vector with respect to matrix {\partial {W}}? Whether it results in a matrix or tensor of higher dimension?

Apart from the sequence equation what will be the result of the partial derivative of a matrix with respect to vector? Say in case of \frac{\partial {W}}{\partial s_{k}} where W is a matrix and s_{k} is a vector?
I just want to understand the math behind them.