There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ (\frac{3}{2})arcsin(\frac{2x}{3}) + (\frac{1}{2})sqrt(9 - 4({x}^{2}))\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{3}{2}arcsin(\frac{2}{3}x) + \frac{1}{2}sqrt(-4x^{2} + 9)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{3}{2}arcsin(\frac{2}{3}x) + \frac{1}{2}sqrt(-4x^{2} + 9)\right)}{dx}\\=&\frac{3}{2}(\frac{(\frac{2}{3})}{((1 - (\frac{2}{3}x)^{2})^{\frac{1}{2}})}) + \frac{\frac{1}{2}(-4*2x + 0)*\frac{1}{2}}{(-4x^{2} + 9)^{\frac{1}{2}}}\\=&\frac{-2x}{(-4x^{2} + 9)^{\frac{1}{2}}} + \frac{1}{(\frac{-4}{9}x^{2} + 1)^{\frac{1}{2}}}\\ \end{split}\end{equation} \]

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