There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ sin(x){\frac{1}{x}}^{2}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{sin(x)}{x^{2}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{sin(x)}{x^{2}}\right)}{dx}\\=&\frac{-2sin(x)}{x^{3}} + \frac{cos(x)}{x^{2}}\\=&\frac{-2sin(x)}{x^{3}} + \frac{cos(x)}{x^{2}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-2sin(x)}{x^{3}} + \frac{cos(x)}{x^{2}}\right)}{dx}\\=&\frac{-2*-3sin(x)}{x^{4}} - \frac{2cos(x)}{x^{3}} + \frac{-2cos(x)}{x^{3}} + \frac{-sin(x)}{x^{2}}\\=&\frac{6sin(x)}{x^{4}} - \frac{4cos(x)}{x^{3}} - \frac{sin(x)}{x^{2}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{6sin(x)}{x^{4}} - \frac{4cos(x)}{x^{3}} - \frac{sin(x)}{x^{2}}\right)}{dx}\\=&\frac{6*-4sin(x)}{x^{5}} + \frac{6cos(x)}{x^{4}} - \frac{4*-3cos(x)}{x^{4}} - \frac{4*-sin(x)}{x^{3}} - \frac{-2sin(x)}{x^{3}} - \frac{cos(x)}{x^{2}}\\=&\frac{-24sin(x)}{x^{5}} + \frac{18cos(x)}{x^{4}} + \frac{6sin(x)}{x^{3}} - \frac{cos(x)}{x^{2}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{-24sin(x)}{x^{5}} + \frac{18cos(x)}{x^{4}} + \frac{6sin(x)}{x^{3}} - \frac{cos(x)}{x^{2}}\right)}{dx}\\=&\frac{-24*-5sin(x)}{x^{6}} - \frac{24cos(x)}{x^{5}} + \frac{18*-4cos(x)}{x^{5}} + \frac{18*-sin(x)}{x^{4}} + \frac{6*-3sin(x)}{x^{4}} + \frac{6cos(x)}{x^{3}} - \frac{-2cos(x)}{x^{3}} - \frac{-sin(x)}{x^{2}}\\=&\frac{120sin(x)}{x^{6}} - \frac{96cos(x)}{x^{5}} - \frac{36sin(x)}{x^{4}} + \frac{8cos(x)}{x^{3}} + \frac{sin(x)}{x^{2}}\\ \end{split}\end{equation} \]

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