There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ sin(\frac{1}{x})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( sin(\frac{1}{x})\right)}{dx}\\=&\frac{cos(\frac{1}{x})*-1}{x^{2}}\\=&\frac{-cos(\frac{1}{x})}{x^{2}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-cos(\frac{1}{x})}{x^{2}}\right)}{dx}\\=&\frac{--2cos(\frac{1}{x})}{x^{3}} - \frac{-sin(\frac{1}{x})*-1}{x^{2}x^{2}}\\=&\frac{2cos(\frac{1}{x})}{x^{3}} - \frac{sin(\frac{1}{x})}{x^{4}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{2cos(\frac{1}{x})}{x^{3}} - \frac{sin(\frac{1}{x})}{x^{4}}\right)}{dx}\\=&\frac{2*-3cos(\frac{1}{x})}{x^{4}} + \frac{2*-sin(\frac{1}{x})*-1}{x^{3}x^{2}} - \frac{-4sin(\frac{1}{x})}{x^{5}} - \frac{cos(\frac{1}{x})*-1}{x^{4}x^{2}}\\=&\frac{-6cos(\frac{1}{x})}{x^{4}} + \frac{6sin(\frac{1}{x})}{x^{5}} + \frac{cos(\frac{1}{x})}{x^{6}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{-6cos(\frac{1}{x})}{x^{4}} + \frac{6sin(\frac{1}{x})}{x^{5}} + \frac{cos(\frac{1}{x})}{x^{6}}\right)}{dx}\\=&\frac{-6*-4cos(\frac{1}{x})}{x^{5}} - \frac{6*-sin(\frac{1}{x})*-1}{x^{4}x^{2}} + \frac{6*-5sin(\frac{1}{x})}{x^{6}} + \frac{6cos(\frac{1}{x})*-1}{x^{5}x^{2}} + \frac{-6cos(\frac{1}{x})}{x^{7}} + \frac{-sin(\frac{1}{x})*-1}{x^{6}x^{2}}\\=&\frac{24cos(\frac{1}{x})}{x^{5}} - \frac{36sin(\frac{1}{x})}{x^{6}} - \frac{12cos(\frac{1}{x})}{x^{7}} + \frac{sin(\frac{1}{x})}{x^{8}}\\ \end{split}\end{equation} \]

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