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

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