There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{sqrt(2 + x - {x}^{2})}{4} + \frac{5arcsin(\frac{(4x - 2)}{5})}{8}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{1}{4}sqrt(x - x^{2} + 2) + \frac{5}{8}arcsin(\frac{4}{5}x - \frac{2}{5})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{1}{4}sqrt(x - x^{2} + 2) + \frac{5}{8}arcsin(\frac{4}{5}x - \frac{2}{5})\right)}{dx}\\=&\frac{\frac{1}{4}(1 - 2x + 0)*\frac{1}{2}}{(x - x^{2} + 2)^{\frac{1}{2}}} + \frac{5}{8}(\frac{(\frac{4}{5} + 0)}{((1 - (\frac{4}{5}x - \frac{2}{5})^{2})^{\frac{1}{2}})})\\=& - \frac{x}{4(x - x^{2} + 2)^{\frac{1}{2}}} + \frac{1}{8(x - x^{2} + 2)^{\frac{1}{2}}} + \frac{1}{2(\frac{-16}{25}x^{2} + \frac{16}{25}x + \frac{21}{25})^{\frac{1}{2}}}\\ \end{split}\end{equation} \]

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