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

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