There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ {(1 - \frac{2}{x})}^{\frac{1}{4}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = (\frac{-2}{x} + 1)^{\frac{1}{4}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( (\frac{-2}{x} + 1)^{\frac{1}{4}}\right)}{dx}\\=&(\frac{\frac{1}{4}(\frac{-2*-1}{x^{2}} + 0)}{(\frac{-2}{x} + 1)^{\frac{3}{4}}})\\=&\frac{1}{2(\frac{-2}{x} + 1)^{\frac{3}{4}}x^{2}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{1}{2(\frac{-2}{x} + 1)^{\frac{3}{4}}x^{2}}\right)}{dx}\\=&\frac{(\frac{\frac{-3}{4}(\frac{-2*-1}{x^{2}} + 0)}{(\frac{-2}{x} + 1)^{\frac{7}{4}}})}{2x^{2}} + \frac{-2}{2(\frac{-2}{x} + 1)^{\frac{3}{4}}x^{3}}\\=&\frac{-3}{4(\frac{-2}{x} + 1)^{\frac{7}{4}}x^{4}} - \frac{1}{(\frac{-2}{x} + 1)^{\frac{3}{4}}x^{3}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{-3}{4(\frac{-2}{x} + 1)^{\frac{7}{4}}x^{4}} - \frac{1}{(\frac{-2}{x} + 1)^{\frac{3}{4}}x^{3}}\right)}{dx}\\=&\frac{-3(\frac{\frac{-7}{4}(\frac{-2*-1}{x^{2}} + 0)}{(\frac{-2}{x} + 1)^{\frac{11}{4}}})}{4x^{4}} - \frac{3*-4}{4(\frac{-2}{x} + 1)^{\frac{7}{4}}x^{5}} - \frac{(\frac{\frac{-3}{4}(\frac{-2*-1}{x^{2}} + 0)}{(\frac{-2}{x} + 1)^{\frac{7}{4}}})}{x^{3}} - \frac{-3}{(\frac{-2}{x} + 1)^{\frac{3}{4}}x^{4}}\\=&\frac{21}{8(\frac{-2}{x} + 1)^{\frac{11}{4}}x^{6}} + \frac{9}{2(\frac{-2}{x} + 1)^{\frac{7}{4}}x^{5}} + \frac{3}{(\frac{-2}{x} + 1)^{\frac{3}{4}}x^{4}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{21}{8(\frac{-2}{x} + 1)^{\frac{11}{4}}x^{6}} + \frac{9}{2(\frac{-2}{x} + 1)^{\frac{7}{4}}x^{5}} + \frac{3}{(\frac{-2}{x} + 1)^{\frac{3}{4}}x^{4}}\right)}{dx}\\=&\frac{21(\frac{\frac{-11}{4}(\frac{-2*-1}{x^{2}} + 0)}{(\frac{-2}{x} + 1)^{\frac{15}{4}}})}{8x^{6}} + \frac{21*-6}{8(\frac{-2}{x} + 1)^{\frac{11}{4}}x^{7}} + \frac{9(\frac{\frac{-7}{4}(\frac{-2*-1}{x^{2}} + 0)}{(\frac{-2}{x} + 1)^{\frac{11}{4}}})}{2x^{5}} + \frac{9*-5}{2(\frac{-2}{x} + 1)^{\frac{7}{4}}x^{6}} + \frac{3(\frac{\frac{-3}{4}(\frac{-2*-1}{x^{2}} + 0)}{(\frac{-2}{x} + 1)^{\frac{7}{4}}})}{x^{4}} + \frac{3*-4}{(\frac{-2}{x} + 1)^{\frac{3}{4}}x^{5}}\\=&\frac{-231}{16(\frac{-2}{x} + 1)^{\frac{15}{4}}x^{8}} - \frac{63}{2(\frac{-2}{x} + 1)^{\frac{11}{4}}x^{7}} - \frac{27}{(\frac{-2}{x} + 1)^{\frac{7}{4}}x^{6}} - \frac{12}{(\frac{-2}{x} + 1)^{\frac{3}{4}}x^{5}}\\ \end{split}\end{equation} \]

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