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

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