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

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