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

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