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

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