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

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