There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ arcsin(\frac{{2}^{\frac{1}{2}}x}{sqrt({x}^{2} + 1)})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = arcsin(\frac{2^{\frac{1}{2}}x}{sqrt(x^{2} + 1)})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( arcsin(\frac{2^{\frac{1}{2}}x}{sqrt(x^{2} + 1)})\right)}{dx}\\=&(\frac{(\frac{2^{\frac{1}{2}}}{sqrt(x^{2} + 1)} + \frac{2^{\frac{1}{2}}x*-(2x + 0)*\frac{1}{2}}{(x^{2} + 1)(x^{2} + 1)^{\frac{1}{2}}})}{((1 - (\frac{2^{\frac{1}{2}}x}{sqrt(x^{2} + 1)})^{2})^{\frac{1}{2}})})\\=&\frac{2^{\frac{1}{2}}}{(\frac{-2x^{2}}{sqrt(x^{2} + 1)^{2}} + 1)^{\frac{1}{2}}sqrt(x^{2} + 1)} - \frac{2^{\frac{1}{2}}x^{2}}{(\frac{-2x^{2}}{sqrt(x^{2} + 1)^{2}} + 1)^{\frac{1}{2}}(x^{2} + 1)^{\frac{3}{2}}}\\ \end{split}\end{equation} \]

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