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

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