There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ ({x}^{3}){\frac{1}{({x}^{2} - 4)}}^{3}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{x^{3}}{(x^{2} - 4)^{3}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{x^{3}}{(x^{2} - 4)^{3}}\right)}{dx}\\=&(\frac{-3(2x + 0)}{(x^{2} - 4)^{4}})x^{3} + \frac{3x^{2}}{(x^{2} - 4)^{3}}\\=&\frac{-6x^{4}}{(x^{2} - 4)^{4}} + \frac{3x^{2}}{(x^{2} - 4)^{3}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-6x^{4}}{(x^{2} - 4)^{4}} + \frac{3x^{2}}{(x^{2} - 4)^{3}}\right)}{dx}\\=&-6(\frac{-4(2x + 0)}{(x^{2} - 4)^{5}})x^{4} - \frac{6*4x^{3}}{(x^{2} - 4)^{4}} + 3(\frac{-3(2x + 0)}{(x^{2} - 4)^{4}})x^{2} + \frac{3*2x}{(x^{2} - 4)^{3}}\\=&\frac{48x^{5}}{(x^{2} - 4)^{5}} - \frac{42x^{3}}{(x^{2} - 4)^{4}} + \frac{6x}{(x^{2} - 4)^{3}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{48x^{5}}{(x^{2} - 4)^{5}} - \frac{42x^{3}}{(x^{2} - 4)^{4}} + \frac{6x}{(x^{2} - 4)^{3}}\right)}{dx}\\=&48(\frac{-5(2x + 0)}{(x^{2} - 4)^{6}})x^{5} + \frac{48*5x^{4}}{(x^{2} - 4)^{5}} - 42(\frac{-4(2x + 0)}{(x^{2} - 4)^{5}})x^{3} - \frac{42*3x^{2}}{(x^{2} - 4)^{4}} + 6(\frac{-3(2x + 0)}{(x^{2} - 4)^{4}})x + \frac{6}{(x^{2} - 4)^{3}}\\=&\frac{-480x^{6}}{(x^{2} - 4)^{6}} + \frac{576x^{4}}{(x^{2} - 4)^{5}} - \frac{162x^{2}}{(x^{2} - 4)^{4}} + \frac{6}{(x^{2} - 4)^{3}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{-480x^{6}}{(x^{2} - 4)^{6}} + \frac{576x^{4}}{(x^{2} - 4)^{5}} - \frac{162x^{2}}{(x^{2} - 4)^{4}} + \frac{6}{(x^{2} - 4)^{3}}\right)}{dx}\\=&-480(\frac{-6(2x + 0)}{(x^{2} - 4)^{7}})x^{6} - \frac{480*6x^{5}}{(x^{2} - 4)^{6}} + 576(\frac{-5(2x + 0)}{(x^{2} - 4)^{6}})x^{4} + \frac{576*4x^{3}}{(x^{2} - 4)^{5}} - 162(\frac{-4(2x + 0)}{(x^{2} - 4)^{5}})x^{2} - \frac{162*2x}{(x^{2} - 4)^{4}} + 6(\frac{-3(2x + 0)}{(x^{2} - 4)^{4}})\\=&\frac{5760x^{7}}{(x^{2} - 4)^{7}} - \frac{8640x^{5}}{(x^{2} - 4)^{6}} + \frac{3600x^{3}}{(x^{2} - 4)^{5}} - \frac{360x}{(x^{2} - 4)^{4}}\\ \end{split}\end{equation} \]

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