There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(3 + 3{({x}^{2} + 2)}^{6})}{(1 - {({x}^{2} + 2)}^{6})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{3(x^{2} + 2)^{6}}{(-(x^{2} + 2)^{6} + 1)} + \frac{3}{(-(x^{2} + 2)^{6} + 1)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{3(x^{2} + 2)^{6}}{(-(x^{2} + 2)^{6} + 1)} + \frac{3}{(-(x^{2} + 2)^{6} + 1)}\right)}{dx}\\=&\frac{3(6(x^{2} + 2)^{5}(2x + 0))}{(-(x^{2} + 2)^{6} + 1)} + 3(x^{2} + 2)^{6}(\frac{-(-(6(x^{2} + 2)^{5}(2x + 0)) + 0)}{(-(x^{2} + 2)^{6} + 1)^{2}}) + 3(\frac{-(-(6(x^{2} + 2)^{5}(2x + 0)) + 0)}{(-(x^{2} + 2)^{6} + 1)^{2}})\\=&\frac{36x^{11}}{(-(x^{2} + 2)^{6} + 1)} + \frac{360x^{9}}{(-(x^{2} + 2)^{6} + 1)} + \frac{1440x^{7}}{(-(x^{2} + 2)^{6} + 1)} + \frac{2880x^{5}}{(-(x^{2} + 2)^{6} + 1)} + \frac{2880x^{3}}{(-(x^{2} + 2)^{6} + 1)} + \frac{1152x}{(-(x^{2} + 2)^{6} + 1)} + \frac{36(x^{2} + 2)^{11}x}{(-(x^{2} + 2)^{6} + 1)^{2}} + \frac{36x^{11}}{(-(x^{2} + 2)^{6} + 1)^{2}} + \frac{360x^{9}}{(-(x^{2} + 2)^{6} + 1)^{2}} + \frac{1440x^{7}}{(-(x^{2} + 2)^{6} + 1)^{2}} + \frac{2880x^{5}}{(-(x^{2} + 2)^{6} + 1)^{2}} + \frac{2880x^{3}}{(-(x^{2} + 2)^{6} + 1)^{2}} + \frac{1152x}{(-(x^{2} + 2)^{6} + 1)^{2}}\\ \end{split}\end{equation} \]

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