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I would like to know, how to change parts of a formula in HoldForm. 
I have the formula <br/>
$$
\underbrace{\prod_{i=1}^N}_{\text{level 4}} \sum_{\sigma_i\in \{-1,1\}}\underbrace{\sum_{\lambda\in \{-1,1\}}}_{\text{level 2}}\underbrace{\frac{\partial}{\partial x_i}}_{\text{level 3}}\underbrace{\exp\left( -\lambda \sigma_i x_i^2\right)(x_i^2-\lambda)}_{\text{level 1}}
$$
and I put it in **HoldForm** such that it is not evaluated.<br/><br/> 1. I would like to work with the level 1 content first, change it by e.g. an expansion while the other parts remain fixed. After that I would like to exchange the level 2 and level 3 operators (if you regard summation as an operation as well) and evaluate only the level 2 - level 1 part with keeping the rest fixed. The result should read
$$
\underbrace{\prod_{i=1}^N}_{\text{level 4}} \sum_{\sigma_i\in \{-1,1\}}\underbrace{\frac{\partial}{\partial x_i}}_{\text{level 3}}\left(\underbrace{\exp\left(\sigma_i x_i^2\right)(x_i^2+1)}_{\text{level 1}}+\underbrace{\exp\left(-\sigma_i x_i^2\right)(x_i^2-1)}_{\text{level 1}}\right)$$
<br/><br/>
2. I would like to keep the order and eveluate the level 2 sum while the level 3 operator is not applied but remains in the HoldForm. 
The result for the second task should read $$
\underbrace{\prod_{i=1}^N}_{\text{level 4}} \sum_{\sigma_i\in \{-1,1\}}\left(\underbrace{\frac{\partial}{\partial x_i}}_{\text{level 3}}\underbrace{\exp\left(\sigma_i x_i^2\right)(x_i^2+1)}_{\text{level 1}}+\underbrace{\frac{\partial}{\partial x_i}}_{\text{level 3}}\underbrace{\exp\left(-\sigma_i x_i^2\right)(x_i^2-1)}_{\text{level 1}}\right)$$
To summarize, there are two questions: How do I evaluate arbitrary things(different level combinations or maybe $N$ or the set of possible $\lambda$'s) and how do I change the operator order within the HoldForm of an overall summation or integration. <br/><br/>