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

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