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

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