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

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