There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ tan(x) - arctan(x)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( tan(x) - arctan(x)\right)}{dx}\\=&sec^{2}(x)(1) - (\frac{(1)}{(1 + (x)^{2})})\\=&sec^{2}(x) - \frac{1}{(x^{2} + 1)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( sec^{2}(x) - \frac{1}{(x^{2} + 1)}\right)}{dx}\\=&2sec^{2}(x)tan(x) - (\frac{-(2x + 0)}{(x^{2} + 1)^{2}})\\=&2tan(x)sec^{2}(x) + \frac{2x}{(x^{2} + 1)^{2}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 2tan(x)sec^{2}(x) + \frac{2x}{(x^{2} + 1)^{2}}\right)}{dx}\\=&2sec^{2}(x)(1)sec^{2}(x) + 2tan(x)*2sec^{2}(x)tan(x) + 2(\frac{-2(2x + 0)}{(x^{2} + 1)^{3}})x + \frac{2}{(x^{2} + 1)^{2}}\\=&2sec^{4}(x) + 4tan^{2}(x)sec^{2}(x) - \frac{8x^{2}}{(x^{2} + 1)^{3}} + \frac{2}{(x^{2} + 1)^{2}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 2sec^{4}(x) + 4tan^{2}(x)sec^{2}(x) - \frac{8x^{2}}{(x^{2} + 1)^{3}} + \frac{2}{(x^{2} + 1)^{2}}\right)}{dx}\\=&2*4sec^{4}(x)tan(x) + 4*2tan(x)sec^{2}(x)(1)sec^{2}(x) + 4tan^{2}(x)*2sec^{2}(x)tan(x) - 8(\frac{-3(2x + 0)}{(x^{2} + 1)^{4}})x^{2} - \frac{8*2x}{(x^{2} + 1)^{3}} + 2(\frac{-2(2x + 0)}{(x^{2} + 1)^{3}})\\=&16tan(x)sec^{4}(x) + 8tan^{3}(x)sec^{2}(x) + \frac{48x^{3}}{(x^{2} + 1)^{4}} - \frac{24x}{(x^{2} + 1)^{3}}\\ \end{split}\end{equation} \]

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