There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(1 - {({x}^{2} + 2)}^{6})}{(1 + {({x}^{2} + 2)}^{6})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = - \frac{(x^{2} + 2)^{6}}{((x^{2} + 2)^{6} + 1)} + \frac{1}{((x^{2} + 2)^{6} + 1)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( - \frac{(x^{2} + 2)^{6}}{((x^{2} + 2)^{6} + 1)} + \frac{1}{((x^{2} + 2)^{6} + 1)}\right)}{dx}\\=& - \frac{(6(x^{2} + 2)^{5}(2x + 0))}{((x^{2} + 2)^{6} + 1)} - (x^{2} + 2)^{6}(\frac{-((6(x^{2} + 2)^{5}(2x + 0)) + 0)}{((x^{2} + 2)^{6} + 1)^{2}}) + (\frac{-((6(x^{2} + 2)^{5}(2x + 0)) + 0)}{((x^{2} + 2)^{6} + 1)^{2}})\\=& - \frac{12x^{11}}{((x^{2} + 2)^{6} + 1)} - \frac{120x^{9}}{((x^{2} + 2)^{6} + 1)} - \frac{480x^{7}}{((x^{2} + 2)^{6} + 1)} - \frac{960x^{5}}{((x^{2} + 2)^{6} + 1)} - \frac{960x^{3}}{((x^{2} + 2)^{6} + 1)} - \frac{384x}{((x^{2} + 2)^{6} + 1)} + \frac{12(x^{2} + 2)^{11}x}{((x^{2} + 2)^{6} + 1)^{2}} - \frac{12x^{11}}{((x^{2} + 2)^{6} + 1)^{2}} - \frac{120x^{9}}{((x^{2} + 2)^{6} + 1)^{2}} - \frac{480x^{7}}{((x^{2} + 2)^{6} + 1)^{2}} - \frac{960x^{5}}{((x^{2} + 2)^{6} + 1)^{2}} - \frac{960x^{3}}{((x^{2} + 2)^{6} + 1)^{2}} - \frac{384x}{((x^{2} + 2)^{6} + 1)^{2}}\\ \end{split}\end{equation} \]

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