There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(1 + {({x}^{2} + 2)}^{2})}{(1 - {({x}^{2} + 2)}^{2})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{x^{4}}{(-x^{4} - 4x^{2} - 3)} + \frac{4x^{2}}{(-x^{4} - 4x^{2} - 3)} + \frac{5}{(-x^{4} - 4x^{2} - 3)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{x^{4}}{(-x^{4} - 4x^{2} - 3)} + \frac{4x^{2}}{(-x^{4} - 4x^{2} - 3)} + \frac{5}{(-x^{4} - 4x^{2} - 3)}\right)}{dx}\\=&(\frac{-(-4x^{3} - 4*2x + 0)}{(-x^{4} - 4x^{2} - 3)^{2}})x^{4} + \frac{4x^{3}}{(-x^{4} - 4x^{2} - 3)} + 4(\frac{-(-4x^{3} - 4*2x + 0)}{(-x^{4} - 4x^{2} - 3)^{2}})x^{2} + \frac{4*2x}{(-x^{4} - 4x^{2} - 3)} + 5(\frac{-(-4x^{3} - 4*2x + 0)}{(-x^{4} - 4x^{2} - 3)^{2}})\\=&\frac{4x^{7}}{(-x^{4} - 4x^{2} - 3)^{2}} + \frac{24x^{5}}{(-x^{4} - 4x^{2} - 3)^{2}} + \frac{4x^{3}}{(-x^{4} - 4x^{2} - 3)} + \frac{52x^{3}}{(-x^{4} - 4x^{2} - 3)^{2}} + \frac{8x}{(-x^{4} - 4x^{2} - 3)} + \frac{40x}{(-x^{4} - 4x^{2} - 3)^{2}}\\ \end{split}\end{equation} \]

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