There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ {(\frac{({x}^{2} - 4)}{({x}^{2} + 4)})}^{4}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{x^{8}}{(x^{2} + 4)^{4}} - \frac{16x^{6}}{(x^{2} + 4)^{4}} + \frac{96x^{4}}{(x^{2} + 4)^{4}} - \frac{256x^{2}}{(x^{2} + 4)^{4}} + \frac{256}{(x^{2} + 4)^{4}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{x^{8}}{(x^{2} + 4)^{4}} - \frac{16x^{6}}{(x^{2} + 4)^{4}} + \frac{96x^{4}}{(x^{2} + 4)^{4}} - \frac{256x^{2}}{(x^{2} + 4)^{4}} + \frac{256}{(x^{2} + 4)^{4}}\right)}{dx}\\=&(\frac{-4(2x + 0)}{(x^{2} + 4)^{5}})x^{8} + \frac{8x^{7}}{(x^{2} + 4)^{4}} - 16(\frac{-4(2x + 0)}{(x^{2} + 4)^{5}})x^{6} - \frac{16*6x^{5}}{(x^{2} + 4)^{4}} + 96(\frac{-4(2x + 0)}{(x^{2} + 4)^{5}})x^{4} + \frac{96*4x^{3}}{(x^{2} + 4)^{4}} - 256(\frac{-4(2x + 0)}{(x^{2} + 4)^{5}})x^{2} - \frac{256*2x}{(x^{2} + 4)^{4}} + 256(\frac{-4(2x + 0)}{(x^{2} + 4)^{5}})\\=&\frac{-8x^{9}}{(x^{2} + 4)^{5}} + \frac{8x^{7}}{(x^{2} + 4)^{4}} + \frac{128x^{7}}{(x^{2} + 4)^{5}} - \frac{96x^{5}}{(x^{2} + 4)^{4}} - \frac{768x^{5}}{(x^{2} + 4)^{5}} + \frac{384x^{3}}{(x^{2} + 4)^{4}} + \frac{2048x^{3}}{(x^{2} + 4)^{5}} - \frac{512x}{(x^{2} + 4)^{4}} - \frac{2048x}{(x^{2} + 4)^{5}}\\ \end{split}\end{equation} \]

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