There are 1 questions in this calculation: for each question, the 5 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 5th\ derivative\ of\ function\ \frac{(1 - x - {x}^{2})}{(1 + x + {x}^{2})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = - \frac{x}{(x + x^{2} + 1)} - \frac{x^{2}}{(x + x^{2} + 1)} + \frac{1}{(x + x^{2} + 1)}\\\\ &\color{blue}{The\ 5th\ derivative\ of\ function:} \\=&\frac{13440x^{6}}{(x + x^{2} + 1)^{6}} + \frac{3840x^{7}}{(x + x^{2} + 1)^{6}} - \frac{19200x^{4}}{(x + x^{2} + 1)^{5}} + \frac{15360x^{5}}{(x + x^{2} + 1)^{6}} - \frac{3600x^{3}}{(x + x^{2} + 1)^{6}} - \frac{7680x^{5}}{(x + x^{2} + 1)^{5}} + \frac{6840x^{2}}{(x + x^{2} + 1)^{4}} - \frac{3480x^{2}}{(x + x^{2} + 1)^{6}} + \frac{4800x^{4}}{(x + x^{2} + 1)^{6}} - \frac{14400x^{3}}{(x + x^{2} + 1)^{5}} - \frac{2400x^{2}}{(x + x^{2} + 1)^{5}} + \frac{4560x^{3}}{(x + x^{2} + 1)^{4}} + \frac{1200x}{(x + x^{2} + 1)^{5}} + \frac{2520x}{(x + x^{2} + 1)^{4}} - \frac{720x}{(x + x^{2} + 1)^{3}} - \frac{1080x}{(x + x^{2} + 1)^{6}} + \frac{120}{(x + x^{2} + 1)^{4}} + \frac{360}{(x + x^{2} + 1)^{5}} - \frac{360}{(x + x^{2} + 1)^{3}} - \frac{120}{(x + x^{2} + 1)^{6}}\\ \end{split}\end{equation} \]

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