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

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