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

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