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

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