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

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