According to the generalized chain rule formula (using this notation: https://math.libretexts.org/Bookshelves/Calculus/Book%3A_Calculus_(OpenStax)/14%3A_Differentiation_of_Functions_of_Several_Variables/14.5%3A_The_Chain_Rule_for_Multivariable_Functions), we have that
$\displaystyle \frac{\partial w}{\partial t_j} = \sum_{i=1}^{m} \frac{\partial w}{\partial x_i} \cdot \frac{\partial x_i}{\partial t_j}.$
Now, I have this expression (for some fixed $k$):
$\displaystyle \sum_{i=1}^{m} \frac{\partial w}{\partial x_i} \cdot \frac{\partial^2 x_i}{\partial t_j \partial t_k}.$
I would like to get rid of the summation. Is there some way to use the generalized chain rule formula here to achieve this?