There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(sqrt(8 - x)xsqrt(x + 8) + 64arcsin(\frac{x}{8}))}{2}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{1}{2}xsqrt(x + 8)sqrt(-x + 8) + 32arcsin(\frac{1}{8}x)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{1}{2}xsqrt(x + 8)sqrt(-x + 8) + 32arcsin(\frac{1}{8}x)\right)}{dx}\\=&\frac{1}{2}sqrt(x + 8)sqrt(-x + 8) + \frac{\frac{1}{2}x(1 + 0)*\frac{1}{2}sqrt(-x + 8)}{(x + 8)^{\frac{1}{2}}} + \frac{\frac{1}{2}xsqrt(x + 8)(-1 + 0)*\frac{1}{2}}{(-x + 8)^{\frac{1}{2}}} + 32(\frac{(\frac{1}{8})}{((1 - (\frac{1}{8}x)^{2})^{\frac{1}{2}})})\\=&\frac{sqrt(x + 8)sqrt(-x + 8)}{2} + \frac{xsqrt(-x + 8)}{4(x + 8)^{\frac{1}{2}}} - \frac{xsqrt(x + 8)}{4(-x + 8)^{\frac{1}{2}}} + \frac{4}{(\frac{-1}{64}x^{2} + 1)^{\frac{1}{2}}}\\ \end{split}\end{equation} \]

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