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

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