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Homework Statement
My question is regarding a single step in a solution to a given problem. The step begins at:
##\large \frac{\partial \alpha _j}{\partial x ^i}
\frac{\partial x^i}{y^p}
\frac{\partial x^j}{\partial y^q} 
\frac{\partial \alpha _j}{\partial x ^i}
\frac{\partial x^i}{\partial y^q}
\frac{x^j}{ \partial y^p}
##
The solution says that the second term has the dummy i and j indices which can be switched in order to factorise which gives us:
##\large \big (\frac{\partial \alpha _j}{\partial x ^i}

\frac{\partial \alpha _i}{\partial x ^j} \big )
\frac{\partial x^i}{\partial y^p}
\frac{\partial x^j}{\partial y^q}
##
1. To clarify, the Einstein summation means that changing the index i in the second term has no implication for the index i in the first term?
2. If the dummies i and j were switched from the first term then I would result in the negative answer. So how does one know beforehand which term for whcih the indices have to be switched?