There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(3 - 3{({x}^{2} + 2)}^{2})}{(1 + {({x}^{2} + 2)}^{2})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = - \frac{3x^{4}}{(x^{4} + 4x^{2} + 5)} - \frac{12x^{2}}{(x^{4} + 4x^{2} + 5)} - \frac{9}{(x^{4} + 4x^{2} + 5)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( - \frac{3x^{4}}{(x^{4} + 4x^{2} + 5)} - \frac{12x^{2}}{(x^{4} + 4x^{2} + 5)} - \frac{9}{(x^{4} + 4x^{2} + 5)}\right)}{dx}\\=& - 3(\frac{-(4x^{3} + 4*2x + 0)}{(x^{4} + 4x^{2} + 5)^{2}})x^{4} - \frac{3*4x^{3}}{(x^{4} + 4x^{2} + 5)} - 12(\frac{-(4x^{3} + 4*2x + 0)}{(x^{4} + 4x^{2} + 5)^{2}})x^{2} - \frac{12*2x}{(x^{4} + 4x^{2} + 5)} - 9(\frac{-(4x^{3} + 4*2x + 0)}{(x^{4} + 4x^{2} + 5)^{2}})\\=&\frac{12x^{7}}{(x^{4} + 4x^{2} + 5)^{2}} + \frac{72x^{5}}{(x^{4} + 4x^{2} + 5)^{2}} - \frac{12x^{3}}{(x^{4} + 4x^{2} + 5)} + \frac{132x^{3}}{(x^{4} + 4x^{2} + 5)^{2}} - \frac{24x}{(x^{4} + 4x^{2} + 5)} + \frac{72x}{(x^{4} + 4x^{2} + 5)^{2}}\\ \end{split}\end{equation} \]

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