There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ arctan(666x)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( arctan(666x)\right)}{dx}\\=&(\frac{(666)}{(1 + (666x)^{2})})\\=&\frac{666}{(443556x^{2} + 1)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{666}{(443556x^{2} + 1)}\right)}{dx}\\=&666(\frac{-(443556*2x + 0)}{(443556x^{2} + 1)^{2}})\\=&\frac{-590816592x}{(443556x^{2} + 1)^{2}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{-590816592x}{(443556x^{2} + 1)^{2}}\right)}{dx}\\=&-590816592(\frac{-2(443556*2x + 0)}{(443556x^{2} + 1)^{3}})x - \frac{590816592}{(443556x^{2} + 1)^{2}}\\=&\frac{1048240977124608x^{2}}{(443556x^{2} + 1)^{3}} - \frac{590816592}{(443556x^{2} + 1)^{2}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{1048240977124608x^{2}}{(443556x^{2} + 1)^{3}} - \frac{590816592}{(443556x^{2} + 1)^{2}}\right)}{dx}\\=&1048240977124608(\frac{-3(443556*2x + 0)}{(443556x^{2} + 1)^{4}})x^{2} + \frac{1048240977124608*2x}{(443556x^{2} + 1)^{3}} - 590816592(\frac{-2(443556*2x + 0)}{(443556x^{2} + 1)^{3}})\\=&\frac{-4263093966753462272x^{3}}{(443556x^{2} + 1)^{4}} + \frac{3144722931373824x}{(443556x^{2} + 1)^{3}}\\ \end{split}\end{equation} \]

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