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

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