There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{4}{(x(1 + {x}^{2}))}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{4}{(x^{3} + x)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{4}{(x^{3} + x)}\right)}{dx}\\=&4(\frac{-(3x^{2} + 1)}{(x^{3} + x)^{2}})\\=&\frac{-12x^{2}}{(x^{3} + x)^{2}} - \frac{4}{(x^{3} + x)^{2}}\\ \end{split}\end{equation} \]

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