There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ (cos(5{x}^{3}) - 1){\frac{1}{x}}^{3}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{cos(5x^{3})}{x^{3}} - \frac{1}{x^{3}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{cos(5x^{3})}{x^{3}} - \frac{1}{x^{3}}\right)}{dx}\\=&\frac{-3cos(5x^{3})}{x^{4}} + \frac{-sin(5x^{3})*5*3x^{2}}{x^{3}} - \frac{-3}{x^{4}}\\=&\frac{-3cos(5x^{3})}{x^{4}} - \frac{15sin(5x^{3})}{x} + \frac{3}{x^{4}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-3cos(5x^{3})}{x^{4}} - \frac{15sin(5x^{3})}{x} + \frac{3}{x^{4}}\right)}{dx}\\=&\frac{-3*-4cos(5x^{3})}{x^{5}} - \frac{3*-sin(5x^{3})*5*3x^{2}}{x^{4}} - \frac{15*-sin(5x^{3})}{x^{2}} - \frac{15cos(5x^{3})*5*3x^{2}}{x} + \frac{3*-4}{x^{5}}\\=&\frac{12cos(5x^{3})}{x^{5}} + \frac{60sin(5x^{3})}{x^{2}} - 225xcos(5x^{3}) - \frac{12}{x^{5}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{12cos(5x^{3})}{x^{5}} + \frac{60sin(5x^{3})}{x^{2}} - 225xcos(5x^{3}) - \frac{12}{x^{5}}\right)}{dx}\\=&\frac{12*-5cos(5x^{3})}{x^{6}} + \frac{12*-sin(5x^{3})*5*3x^{2}}{x^{5}} + \frac{60*-2sin(5x^{3})}{x^{3}} + \frac{60cos(5x^{3})*5*3x^{2}}{x^{2}} - 225cos(5x^{3}) - 225x*-sin(5x^{3})*5*3x^{2} - \frac{12*-5}{x^{6}}\\=&\frac{-60cos(5x^{3})}{x^{6}} - \frac{300sin(5x^{3})}{x^{3}} + 675cos(5x^{3}) + 3375x^{3}sin(5x^{3}) + \frac{60}{x^{6}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{-60cos(5x^{3})}{x^{6}} - \frac{300sin(5x^{3})}{x^{3}} + 675cos(5x^{3}) + 3375x^{3}sin(5x^{3}) + \frac{60}{x^{6}}\right)}{dx}\\=&\frac{-60*-6cos(5x^{3})}{x^{7}} - \frac{60*-sin(5x^{3})*5*3x^{2}}{x^{6}} - \frac{300*-3sin(5x^{3})}{x^{4}} - \frac{300cos(5x^{3})*5*3x^{2}}{x^{3}} + 675*-sin(5x^{3})*5*3x^{2} + 3375*3x^{2}sin(5x^{3}) + 3375x^{3}cos(5x^{3})*5*3x^{2} + \frac{60*-6}{x^{7}}\\=&\frac{360cos(5x^{3})}{x^{7}} + \frac{1800sin(5x^{3})}{x^{4}} - \frac{4500cos(5x^{3})}{x} + 50625x^{5}cos(5x^{3}) - \frac{360}{x^{7}}\\ \end{split}\end{equation} \]

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