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

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