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

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