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

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