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

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