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Partial derivative of $γ^o$ with respect to $τ$

Values for calculation

$ n^o $
$ J^o $
$ \{τ\in\mathbb{R}\mid τ>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ τ $
$ \text{Region} $

Calculation

Partial derivative of $ γ^o $ with respect to $ τ $

$\text{if }\ \text{Region}= 2$
$\text{if }\ \text{Region}= 2$
Equations in LaTeX code
\text{if }\ \text{Region}= 2
$$γ^o_τ=\sum_{i=1}^{9}{n^o[i]\cdot J^o[i]\cdot τ^{J^o[i]-1}}$$
$γ^o_τ=\sum_{i=1}^{9}{n^o[i]\cdot J^o[i]\cdot τ^{J^o[i]-1}}$
Equations in LaTeX code
γ^o_τ=\sum_{i=1}^{9}{n^o[i]\cdot J^o[i]\cdot τ^{J^o[i]-1}}
$\text{else if }\ \text{Region}= 5$
$\text{else if }\ \text{Region}= 5$
Equations in LaTeX code
\text{else if }\ \text{Region}= 5
$$γ^o_τ=\sum_{i=1}^{6}{n^o[i]\cdot J^o[i]\cdot τ^{J^o[i]-1}}$$
$γ^o_τ=\sum_{i=1}^{6}{n^o[i]\cdot J^o[i]\cdot τ^{J^o[i]-1}}$
Equations in LaTeX code
γ^o_τ=\sum_{i=1}^{6}{n^o[i]\cdot J^o[i]\cdot τ^{J^o[i]-1}}
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$γ^o_τ=0$$
$γ^o_τ=0$
Equations in LaTeX code
γ^o_τ=0
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