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

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