There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{({(x + \frac{4}{x})}^{3})}{(8(x - \frac{4}{x}))}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{x^{3}}{(8x - \frac{32}{x})} + \frac{12x}{(8x - \frac{32}{x})} + \frac{48}{(8x - \frac{32}{x})x} + \frac{64}{(8x - \frac{32}{x})x^{3}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{x^{3}}{(8x - \frac{32}{x})} + \frac{12x}{(8x - \frac{32}{x})} + \frac{48}{(8x - \frac{32}{x})x} + \frac{64}{(8x - \frac{32}{x})x^{3}}\right)}{dx}\\=&(\frac{-(8 - \frac{32*-1}{x^{2}})}{(8x - \frac{32}{x})^{2}})x^{3} + \frac{3x^{2}}{(8x - \frac{32}{x})} + 12(\frac{-(8 - \frac{32*-1}{x^{2}})}{(8x - \frac{32}{x})^{2}})x + \frac{12}{(8x - \frac{32}{x})} + \frac{48(\frac{-(8 - \frac{32*-1}{x^{2}})}{(8x - \frac{32}{x})^{2}})}{x} + \frac{48*-1}{(8x - \frac{32}{x})x^{2}} + \frac{64(\frac{-(8 - \frac{32*-1}{x^{2}})}{(8x - \frac{32}{x})^{2}})}{x^{3}} + \frac{64*-3}{(8x - \frac{32}{x})x^{4}}\\=&\frac{-128x}{(8x - \frac{32}{x})^{2}} - \frac{768}{(8x - \frac{32}{x})^{2}x} + \frac{3x^{2}}{(8x - \frac{32}{x})} - \frac{2048}{(8x - \frac{32}{x})^{2}x^{3}} - \frac{2048}{(8x - \frac{32}{x})^{2}x^{5}} - \frac{48}{(8x - \frac{32}{x})x^{2}} - \frac{8x^{3}}{(8x - \frac{32}{x})^{2}} - \frac{192}{(8x - \frac{32}{x})x^{4}} + \frac{12}{(8x - \frac{32}{x})}\\ \end{split}\end{equation} \]

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