There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ {x}^{2}(x - 3){\frac{1}{(x - 1)}}^{3}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{x^{3}}{(x - 1)^{3}} - \frac{3x^{2}}{(x - 1)^{3}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{x^{3}}{(x - 1)^{3}} - \frac{3x^{2}}{(x - 1)^{3}}\right)}{dx}\\=&(\frac{-3(1 + 0)}{(x - 1)^{4}})x^{3} + \frac{3x^{2}}{(x - 1)^{3}} - 3(\frac{-3(1 + 0)}{(x - 1)^{4}})x^{2} - \frac{3*2x}{(x - 1)^{3}}\\=&\frac{-3x^{3}}{(x - 1)^{4}} + \frac{3x^{2}}{(x - 1)^{3}} + \frac{9x^{2}}{(x - 1)^{4}} - \frac{6x}{(x - 1)^{3}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-3x^{3}}{(x - 1)^{4}} + \frac{3x^{2}}{(x - 1)^{3}} + \frac{9x^{2}}{(x - 1)^{4}} - \frac{6x}{(x - 1)^{3}}\right)}{dx}\\=&-3(\frac{-4(1 + 0)}{(x - 1)^{5}})x^{3} - \frac{3*3x^{2}}{(x - 1)^{4}} + 3(\frac{-3(1 + 0)}{(x - 1)^{4}})x^{2} + \frac{3*2x}{(x - 1)^{3}} + 9(\frac{-4(1 + 0)}{(x - 1)^{5}})x^{2} + \frac{9*2x}{(x - 1)^{4}} - 6(\frac{-3(1 + 0)}{(x - 1)^{4}})x - \frac{6}{(x - 1)^{3}}\\=&\frac{12x^{3}}{(x - 1)^{5}} - \frac{18x^{2}}{(x - 1)^{4}} + \frac{6x}{(x - 1)^{3}} - \frac{36x^{2}}{(x - 1)^{5}} + \frac{36x}{(x - 1)^{4}} - \frac{6}{(x - 1)^{3}}\\ \end{split}\end{equation} \]

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