There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ \frac{1}{({x}^{2}{(x - 1)}^{2})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{1}{(x - 1)^{2}x^{2}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{1}{(x - 1)^{2}x^{2}}\right)}{dx}\\=&\frac{(\frac{-2(1 + 0)}{(x - 1)^{3}})}{x^{2}} + \frac{-2}{(x - 1)^{2}x^{3}}\\=&\frac{-2}{(x - 1)^{3}x^{2}} - \frac{2}{(x - 1)^{2}x^{3}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-2}{(x - 1)^{3}x^{2}} - \frac{2}{(x - 1)^{2}x^{3}}\right)}{dx}\\=&\frac{-2(\frac{-3(1 + 0)}{(x - 1)^{4}})}{x^{2}} - \frac{2*-2}{(x - 1)^{3}x^{3}} - \frac{2(\frac{-2(1 + 0)}{(x - 1)^{3}})}{x^{3}} - \frac{2*-3}{(x - 1)^{2}x^{4}}\\=&\frac{6}{(x - 1)^{4}x^{2}} + \frac{8}{(x - 1)^{3}x^{3}} + \frac{6}{(x - 1)^{2}x^{4}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{6}{(x - 1)^{4}x^{2}} + \frac{8}{(x - 1)^{3}x^{3}} + \frac{6}{(x - 1)^{2}x^{4}}\right)}{dx}\\=&\frac{6(\frac{-4(1 + 0)}{(x - 1)^{5}})}{x^{2}} + \frac{6*-2}{(x - 1)^{4}x^{3}} + \frac{8(\frac{-3(1 + 0)}{(x - 1)^{4}})}{x^{3}} + \frac{8*-3}{(x - 1)^{3}x^{4}} + \frac{6(\frac{-2(1 + 0)}{(x - 1)^{3}})}{x^{4}} + \frac{6*-4}{(x - 1)^{2}x^{5}}\\=&\frac{-24}{(x - 1)^{5}x^{2}} - \frac{36}{(x - 1)^{4}x^{3}} - \frac{36}{(x - 1)^{3}x^{4}} - \frac{24}{(x - 1)^{2}x^{5}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{-24}{(x - 1)^{5}x^{2}} - \frac{36}{(x - 1)^{4}x^{3}} - \frac{36}{(x - 1)^{3}x^{4}} - \frac{24}{(x - 1)^{2}x^{5}}\right)}{dx}\\=&\frac{-24(\frac{-5(1 + 0)}{(x - 1)^{6}})}{x^{2}} - \frac{24*-2}{(x - 1)^{5}x^{3}} - \frac{36(\frac{-4(1 + 0)}{(x - 1)^{5}})}{x^{3}} - \frac{36*-3}{(x - 1)^{4}x^{4}} - \frac{36(\frac{-3(1 + 0)}{(x - 1)^{4}})}{x^{4}} - \frac{36*-4}{(x - 1)^{3}x^{5}} - \frac{24(\frac{-2(1 + 0)}{(x - 1)^{3}})}{x^{5}} - \frac{24*-5}{(x - 1)^{2}x^{6}}\\=&\frac{120}{(x - 1)^{6}x^{2}} + \frac{192}{(x - 1)^{5}x^{3}} + \frac{216}{(x - 1)^{4}x^{4}} + \frac{192}{(x - 1)^{3}x^{5}} + \frac{120}{(x - 1)^{2}x^{6}}\\ \end{split}\end{equation} \]

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