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

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