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

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