There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ 2 - \frac{2}{(1 + {x}^{2})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = - \frac{2}{(x^{2} + 1)} + 2\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( - \frac{2}{(x^{2} + 1)} + 2\right)}{dx}\\=& - 2(\frac{-(2x + 0)}{(x^{2} + 1)^{2}}) + 0\\=&\frac{4x}{(x^{2} + 1)^{2}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{4x}{(x^{2} + 1)^{2}}\right)}{dx}\\=&4(\frac{-2(2x + 0)}{(x^{2} + 1)^{3}})x + \frac{4}{(x^{2} + 1)^{2}}\\=& - \frac{16x^{2}}{(x^{2} + 1)^{3}} + \frac{4}{(x^{2} + 1)^{2}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( - \frac{16x^{2}}{(x^{2} + 1)^{3}} + \frac{4}{(x^{2} + 1)^{2}}\right)}{dx}\\=& - 16(\frac{-3(2x + 0)}{(x^{2} + 1)^{4}})x^{2} - \frac{16*2x}{(x^{2} + 1)^{3}} + 4(\frac{-2(2x + 0)}{(x^{2} + 1)^{3}})\\=&\frac{96x^{3}}{(x^{2} + 1)^{4}} - \frac{48x}{(x^{2} + 1)^{3}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{96x^{3}}{(x^{2} + 1)^{4}} - \frac{48x}{(x^{2} + 1)^{3}}\right)}{dx}\\=&96(\frac{-4(2x + 0)}{(x^{2} + 1)^{5}})x^{3} + \frac{96*3x^{2}}{(x^{2} + 1)^{4}} - 48(\frac{-3(2x + 0)}{(x^{2} + 1)^{4}})x - \frac{48}{(x^{2} + 1)^{3}}\\=& - \frac{768x^{4}}{(x^{2} + 1)^{5}} + \frac{576x^{2}}{(x^{2} + 1)^{4}} - \frac{48}{(x^{2} + 1)^{3}}\\ \end{split}\end{equation} \]

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