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

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