There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ \frac{({(x - 1)}^{3})}{({x}^{3}({x}^{2} - 1))}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{x^{3}}{(x^{5} - x^{3})} - \frac{3x^{2}}{(x^{5} - x^{3})} + \frac{3x}{(x^{5} - x^{3})} - \frac{1}{(x^{5} - x^{3})}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{x^{3}}{(x^{5} - x^{3})} - \frac{3x^{2}}{(x^{5} - x^{3})} + \frac{3x}{(x^{5} - x^{3})} - \frac{1}{(x^{5} - x^{3})}\right)}{dx}\\=&(\frac{-(5x^{4} - 3x^{2})}{(x^{5} - x^{3})^{2}})x^{3} + \frac{3x^{2}}{(x^{5} - x^{3})} - 3(\frac{-(5x^{4} - 3x^{2})}{(x^{5} - x^{3})^{2}})x^{2} - \frac{3*2x}{(x^{5} - x^{3})} + 3(\frac{-(5x^{4} - 3x^{2})}{(x^{5} - x^{3})^{2}})x + \frac{3}{(x^{5} - x^{3})} - (\frac{-(5x^{4} - 3x^{2})}{(x^{5} - x^{3})^{2}})\\=&\frac{-5x^{7}}{(x^{5} - x^{3})^{2}} - \frac{12x^{5}}{(x^{5} - x^{3})^{2}} + \frac{3x^{2}}{(x^{5} - x^{3})} + \frac{15x^{6}}{(x^{5} - x^{3})^{2}} - \frac{4x^{4}}{(x^{5} - x^{3})^{2}} - \frac{6x}{(x^{5} - x^{3})} + \frac{9x^{3}}{(x^{5} - x^{3})^{2}} - \frac{3x^{2}}{(x^{5} - x^{3})^{2}} + \frac{3}{(x^{5} - x^{3})}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-5x^{7}}{(x^{5} - x^{3})^{2}} - \frac{12x^{5}}{(x^{5} - x^{3})^{2}} + \frac{3x^{2}}{(x^{5} - x^{3})} + \frac{15x^{6}}{(x^{5} - x^{3})^{2}} - \frac{4x^{4}}{(x^{5} - x^{3})^{2}} - \frac{6x}{(x^{5} - x^{3})} + \frac{9x^{3}}{(x^{5} - x^{3})^{2}} - \frac{3x^{2}}{(x^{5} - x^{3})^{2}} + \frac{3}{(x^{5} - x^{3})}\right)}{dx}\\=&-5(\frac{-2(5x^{4} - 3x^{2})}{(x^{5} - x^{3})^{3}})x^{7} - \frac{5*7x^{6}}{(x^{5} - x^{3})^{2}} - 12(\frac{-2(5x^{4} - 3x^{2})}{(x^{5} - x^{3})^{3}})x^{5} - \frac{12*5x^{4}}{(x^{5} - x^{3})^{2}} + 3(\frac{-(5x^{4} - 3x^{2})}{(x^{5} - x^{3})^{2}})x^{2} + \frac{3*2x}{(x^{5} - x^{3})} + 15(\frac{-2(5x^{4} - 3x^{2})}{(x^{5} - x^{3})^{3}})x^{6} + \frac{15*6x^{5}}{(x^{5} - x^{3})^{2}} - 4(\frac{-2(5x^{4} - 3x^{2})}{(x^{5} - x^{3})^{3}})x^{4} - \frac{4*4x^{3}}{(x^{5} - x^{3})^{2}} - 6(\frac{-(5x^{4} - 3x^{2})}{(x^{5} - x^{3})^{2}})x - \frac{6}{(x^{5} - x^{3})} + 9(\frac{-2(5x^{4} - 3x^{2})}{(x^{5} - x^{3})^{3}})x^{3} + \frac{9*3x^{2}}{(x^{5} - x^{3})^{2}} - 3(\frac{-2(5x^{4} - 3x^{2})}{(x^{5} - x^{3})^{3}})x^{2} - \frac{3*2x}{(x^{5} - x^{3})^{2}} + 3(\frac{-(5x^{4} - 3x^{2})}{(x^{5} - x^{3})^{2}})\\=&\frac{50x^{11}}{(x^{5} - x^{3})^{3}} + \frac{90x^{9}}{(x^{5} - x^{3})^{3}} - \frac{50x^{6}}{(x^{5} - x^{3})^{2}} - \frac{162x^{7}}{(x^{5} - x^{3})^{3}} - \frac{66x^{4}}{(x^{5} - x^{3})^{2}} + \frac{6x}{(x^{5} - x^{3})} - \frac{150x^{10}}{(x^{5} - x^{3})^{3}} + \frac{130x^{8}}{(x^{5} - x^{3})^{3}} + \frac{120x^{5}}{(x^{5} - x^{3})^{2}} + \frac{6x^{6}}{(x^{5} - x^{3})^{3}} - \frac{34x^{3}}{(x^{5} - x^{3})^{2}} + \frac{36x^{2}}{(x^{5} - x^{3})^{2}} + \frac{54x^{5}}{(x^{5} - x^{3})^{3}} - \frac{6x}{(x^{5} - x^{3})^{2}} - \frac{18x^{4}}{(x^{5} - x^{3})^{3}} - \frac{6}{(x^{5} - x^{3})}\\ \end{split}\end{equation} \]

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