There are 1 questions in this calculation: for each question, the 1 derivative of t is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ {10}^{-10}e^{-{(\frac{(t - 3T)}{T})}^{2}}\ with\ respect\ to\ t：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{1}{10000000000}e^{\frac{-t^{2}}{T^{2}} + \frac{6t}{T} - 9}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{1}{10000000000}e^{\frac{-t^{2}}{T^{2}} + \frac{6t}{T} - 9}\right)}{dt}\\=&\frac{1}{10000000000}e^{\frac{-t^{2}}{T^{2}} + \frac{6t}{T} - 9}(\frac{-2t}{T^{2}} + \frac{6}{T} + 0)\\=&\frac{-te^{\frac{-t^{2}}{T^{2}} + \frac{6t}{T} - 9}}{5000000000T^{2}} + \frac{3e^{\frac{-t^{2}}{T^{2}} + \frac{6t}{T} - 9}}{5000000000T}\\ \end{split}\end{equation} \]

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