There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{({(1 + {a}^{2}{\frac{1}{x}}^{2})}^{(\frac{2}{3})}){a}^{2}}{2}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{1}{2}(\frac{a^{2}}{x^{2}} + 1)^{\frac{2}{3}}a^{2}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{1}{2}(\frac{a^{2}}{x^{2}} + 1)^{\frac{2}{3}}a^{2}\right)}{dx}\\=&\frac{1}{2}(\frac{\frac{2}{3}(\frac{a^{2}*-2}{x^{3}} + 0)}{(\frac{a^{2}}{x^{2}} + 1)^{\frac{1}{3}}})a^{2} + 0\\=&\frac{-2a^{4}}{3(\frac{a^{2}}{x^{2}} + 1)^{\frac{1}{3}}x^{3}}\\ \end{split}\end{equation} \]

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