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

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