There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ (\frac{2}{3})arcsin(\frac{1}{2}{x}^{(\frac{3}{2})})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{2}{3}arcsin(\frac{1}{2}x^{\frac{3}{2}})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{2}{3}arcsin(\frac{1}{2}x^{\frac{3}{2}})\right)}{dx}\\=&\frac{2}{3}(\frac{(\frac{1}{2}*\frac{3}{2}x^{\frac{1}{2}})}{((1 - (\frac{1}{2}x^{\frac{3}{2}})^{2})^{\frac{1}{2}})})\\=&\frac{x^{\frac{1}{2}}}{2(\frac{-1}{4}x^{3} + 1)^{\frac{1}{2}}}\\ \end{split}\end{equation} \]

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