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

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