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

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