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

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