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

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