There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(8x + 12)}{(4{x}^{2} + 1)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{8x}{(4x^{2} + 1)} + \frac{12}{(4x^{2} + 1)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{8x}{(4x^{2} + 1)} + \frac{12}{(4x^{2} + 1)}\right)}{dx}\\=&8(\frac{-(4*2x + 0)}{(4x^{2} + 1)^{2}})x + \frac{8}{(4x^{2} + 1)} + 12(\frac{-(4*2x + 0)}{(4x^{2} + 1)^{2}})\\=&\frac{-64x^{2}}{(4x^{2} + 1)^{2}} - \frac{96x}{(4x^{2} + 1)^{2}} + \frac{8}{(4x^{2} + 1)}\\ \end{split}\end{equation} \]

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