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

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