Hi all, Would you be able to further explain how to obtain the differentiation of the RHS of the equation? I'm unsure why the summation term for i for both terms disappears. Thanks!
In a more general case let's consider: \[I = \sum_{i=1}^{n}\sum_{j=1}^{n}x_i x_j\] When taking partial derivatives with respect to \(x_k\) we assume that all other \(x\)'s remain constant. So the only terms that will have a non-zero value are those which involve \(x_k\) specifically, ie: \begin{align} \frac{\partial I}{\partial x_k} & = \sum_{i=1}^{n}\sum_{j=1}^{n}\frac{\partial x_i x_j}{\partial x_k}\ \\ & = \underbrace{\sum_{i=1}^{n}x_i}_{\rm{when}\: j=k} + \underbrace{\sum_{j=1}^{n}x_j}_{\rm{when}\: i=k} \\ & = 2\sum_{i=1}^{n}x_i \\ \end{align} Please let me know if that's not what you're asking about.
