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Partial derivative of $φ$ with respect to $τ$

Values for calculation

$n$
$δ$
$I$
$J$
$τ$
$\text{Region}$

Calculation

Partial derivative of $ φ $ with respect to $ τ $

$\text{if }\ \text{Region}= 3$
$\text{if }\ \text{Region}= 3$
Equations in LaTeX code
\text{if }\ \text{Region}= 3
$$φ_τ=\sum_{i=2}^{40}{n[i]\cdot δ^{I[i]}\cdot J[i]\cdot τ^{J[i]-1}}$$
$φ_τ=\sum_{i=2}^{40}{n[i]\cdot δ^{I[i]}\cdot J[i]\cdot τ^{J[i]-1}}$
Equations in LaTeX code
φ_τ=\sum_{i=2}^{40}{n[i]\cdot δ^{I[i]}\cdot J[i]\cdot τ^{J[i]-1}}
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$φ_τ=0$$
$φ_τ=0$
Equations in LaTeX code
φ_τ=0
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