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

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