There are 1 questions in this calculation: for each question, the 3 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ third\ derivative\ of\ function\ (x - 2)*2 - x(x - 1)ln(x - 1)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = - x^{2}ln(x - 1) + xln(x - 1) + 2x - 4\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( - x^{2}ln(x - 1) + xln(x - 1) + 2x - 4\right)}{dx}\\=& - 2xln(x - 1) - \frac{x^{2}(1 + 0)}{(x - 1)} + ln(x - 1) + \frac{x(1 + 0)}{(x - 1)} + 2 + 0\\=& - 2xln(x - 1) - \frac{x^{2}}{(x - 1)} + ln(x - 1) + \frac{x}{(x - 1)} + 2\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( - 2xln(x - 1) - \frac{x^{2}}{(x - 1)} + ln(x - 1) + \frac{x}{(x - 1)} + 2\right)}{dx}\\=& - 2ln(x - 1) - \frac{2x(1 + 0)}{(x - 1)} - (\frac{-(1 + 0)}{(x - 1)^{2}})x^{2} - \frac{2x}{(x - 1)} + \frac{(1 + 0)}{(x - 1)} + (\frac{-(1 + 0)}{(x - 1)^{2}})x + \frac{1}{(x - 1)} + 0\\=& - 2ln(x - 1) - \frac{4x}{(x - 1)} + \frac{x^{2}}{(x - 1)^{2}} - \frac{x}{(x - 1)^{2}} + \frac{2}{(x - 1)}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( - 2ln(x - 1) - \frac{4x}{(x - 1)} + \frac{x^{2}}{(x - 1)^{2}} - \frac{x}{(x - 1)^{2}} + \frac{2}{(x - 1)}\right)}{dx}\\=& - \frac{2(1 + 0)}{(x - 1)} - 4(\frac{-(1 + 0)}{(x - 1)^{2}})x - \frac{4}{(x - 1)} + (\frac{-2(1 + 0)}{(x - 1)^{3}})x^{2} + \frac{2x}{(x - 1)^{2}} - (\frac{-2(1 + 0)}{(x - 1)^{3}})x - \frac{1}{(x - 1)^{2}} + 2(\frac{-(1 + 0)}{(x - 1)^{2}})\\=&\frac{6x}{(x - 1)^{2}} - \frac{2x^{2}}{(x - 1)^{3}} + \frac{2x}{(x - 1)^{3}} - \frac{3}{(x - 1)^{2}} - \frac{6}{(x - 1)}\\ \end{split}\end{equation} \]

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