I have a question regarding how to evaluate the following expression:
$$\frac{\partial }{\partial x_{i}}\sum_{j=1}^{m} \sum_{k=1}^{m} \frac{1}{2}x_{j}x_{k}\sigma_{jk}$$
Can someone explain the process of working this out. I think all terms where j is not equal to I should disappear but I cannot seem to get the answer. Shown below:
$$\sum_{j=1}^{m} x_{j}\sigma_{ij}$$
I am particular confused as to why the factor of one halve disappears. Any help or pointers would be great.
After working some of this through, I believe that the answer is only true if $\sigma_{jk} = \sigma_{kj}$.