There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ ln((2x){\frac{1}{(({x}^{2}) + 1)}}^{3})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = ln(\frac{2x}{(x^{2} + 1)^{3}})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( ln(\frac{2x}{(x^{2} + 1)^{3}})\right)}{dx}\\=&\frac{(2(\frac{-3(2x + 0)}{(x^{2} + 1)^{4}})x + \frac{2}{(x^{2} + 1)^{3}})}{(\frac{2x}{(x^{2} + 1)^{3}})}\\=&\frac{-6x}{(x^{2} + 1)} + \frac{1}{x}\\ \end{split}\end{equation} \]

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