There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ 3arcsin(sqrt(\frac{(3 + 2x)}{6})) + (\frac{1}{2})sqrt(9 - 4{x}^{2})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 3arcsin(sqrt(\frac{1}{3}x + \frac{1}{2})) + \frac{1}{2}sqrt(-4x^{2} + 9)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 3arcsin(sqrt(\frac{1}{3}x + \frac{1}{2})) + \frac{1}{2}sqrt(-4x^{2} + 9)\right)}{dx}\\=&3(\frac{(\frac{(\frac{1}{3} + 0)*\frac{1}{2}}{(\frac{1}{3}x + \frac{1}{2})^{\frac{1}{2}}})}{((1 - (sqrt(\frac{1}{3}x + \frac{1}{2}))^{2})^{\frac{1}{2}})}) + \frac{\frac{1}{2}(-4*2x + 0)*\frac{1}{2}}{(-4x^{2} + 9)^{\frac{1}{2}}}\\=&\frac{1}{2(-sqrt(\frac{1}{3}x + \frac{1}{2})^{2} + 1)^{\frac{1}{2}}(\frac{1}{3}x + \frac{1}{2})^{\frac{1}{2}}} - \frac{2x}{(-4x^{2} + 9)^{\frac{1}{2}}}\\ \end{split}\end{equation} \]

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