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

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