There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ \frac{{(x - 3)}^{3}}{(x - 1)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{x^{3}}{(x - 1)} - \frac{9x^{2}}{(x - 1)} + \frac{27x}{(x - 1)} - \frac{27}{(x - 1)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{x^{3}}{(x - 1)} - \frac{9x^{2}}{(x - 1)} + \frac{27x}{(x - 1)} - \frac{27}{(x - 1)}\right)}{dx}\\=&(\frac{-(1 + 0)}{(x - 1)^{2}})x^{3} + \frac{3x^{2}}{(x - 1)} - 9(\frac{-(1 + 0)}{(x - 1)^{2}})x^{2} - \frac{9*2x}{(x - 1)} + 27(\frac{-(1 + 0)}{(x - 1)^{2}})x + \frac{27}{(x - 1)} - 27(\frac{-(1 + 0)}{(x - 1)^{2}})\\=&\frac{-x^{3}}{(x - 1)^{2}} + \frac{3x^{2}}{(x - 1)} + \frac{9x^{2}}{(x - 1)^{2}} - \frac{18x}{(x - 1)} - \frac{27x}{(x - 1)^{2}} + \frac{27}{(x - 1)^{2}} + \frac{27}{(x - 1)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-x^{3}}{(x - 1)^{2}} + \frac{3x^{2}}{(x - 1)} + \frac{9x^{2}}{(x - 1)^{2}} - \frac{18x}{(x - 1)} - \frac{27x}{(x - 1)^{2}} + \frac{27}{(x - 1)^{2}} + \frac{27}{(x - 1)}\right)}{dx}\\=&-(\frac{-2(1 + 0)}{(x - 1)^{3}})x^{3} - \frac{3x^{2}}{(x - 1)^{2}} + 3(\frac{-(1 + 0)}{(x - 1)^{2}})x^{2} + \frac{3*2x}{(x - 1)} + 9(\frac{-2(1 + 0)}{(x - 1)^{3}})x^{2} + \frac{9*2x}{(x - 1)^{2}} - 18(\frac{-(1 + 0)}{(x - 1)^{2}})x - \frac{18}{(x - 1)} - 27(\frac{-2(1 + 0)}{(x - 1)^{3}})x - \frac{27}{(x - 1)^{2}} + 27(\frac{-2(1 + 0)}{(x - 1)^{3}}) + 27(\frac{-(1 + 0)}{(x - 1)^{2}})\\=&\frac{2x^{3}}{(x - 1)^{3}} - \frac{6x^{2}}{(x - 1)^{2}} + \frac{6x}{(x - 1)} - \frac{18x^{2}}{(x - 1)^{3}} + \frac{36x}{(x - 1)^{2}} + \frac{54x}{(x - 1)^{3}} - \frac{54}{(x - 1)^{3}} - \frac{54}{(x - 1)^{2}} - \frac{18}{(x - 1)}\\ \end{split}\end{equation} \]

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