There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(1 + 3x){\frac{1}{(4 + 5{x}^{2})}}^{1}}{2}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{\frac{3}{2}x}{(5x^{2} + 4)} + \frac{\frac{1}{2}}{(5x^{2} + 4)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{\frac{3}{2}x}{(5x^{2} + 4)} + \frac{\frac{1}{2}}{(5x^{2} + 4)}\right)}{dx}\\=&\frac{3}{2}(\frac{-(5*2x + 0)}{(5x^{2} + 4)^{2}})x + \frac{\frac{3}{2}}{(5x^{2} + 4)} + \frac{1}{2}(\frac{-(5*2x + 0)}{(5x^{2} + 4)^{2}})\\=& - \frac{15x^{2}}{(5x^{2} + 4)^{2}} - \frac{5x}{(5x^{2} + 4)^{2}} + \frac{3}{2(5x^{2} + 4)}\\ \end{split}\end{equation} \]

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