There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ 10 - Aarctan(ax)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = - Aarctan(ax) + 10\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( - Aarctan(ax) + 10\right)}{dx}\\=& - A(\frac{(a)}{(1 + (ax)^{2})}) + 0\\=& - \frac{Aa}{(a^{2}x^{2} + 1)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( - \frac{Aa}{(a^{2}x^{2} + 1)}\right)}{dx}\\=& - (\frac{-(a^{2}*2x + 0)}{(a^{2}x^{2} + 1)^{2}})Aa + 0\\=&\frac{2Aa^{3}x}{(a^{2}x^{2} + 1)^{2}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{2Aa^{3}x}{(a^{2}x^{2} + 1)^{2}}\right)}{dx}\\=&2(\frac{-2(a^{2}*2x + 0)}{(a^{2}x^{2} + 1)^{3}})Aa^{3}x + \frac{2Aa^{3}}{(a^{2}x^{2} + 1)^{2}}\\=& - \frac{8Aa^{5}x^{2}}{(a^{2}x^{2} + 1)^{3}} + \frac{2Aa^{3}}{(a^{2}x^{2} + 1)^{2}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( - \frac{8Aa^{5}x^{2}}{(a^{2}x^{2} + 1)^{3}} + \frac{2Aa^{3}}{(a^{2}x^{2} + 1)^{2}}\right)}{dx}\\=& - 8(\frac{-3(a^{2}*2x + 0)}{(a^{2}x^{2} + 1)^{4}})Aa^{5}x^{2} - \frac{8Aa^{5}*2x}{(a^{2}x^{2} + 1)^{3}} + 2(\frac{-2(a^{2}*2x + 0)}{(a^{2}x^{2} + 1)^{3}})Aa^{3} + 0\\=&\frac{48Aa^{7}x^{3}}{(a^{2}x^{2} + 1)^{4}} - \frac{24Aa^{5}x}{(a^{2}x^{2} + 1)^{3}}\\ \end{split}\end{equation} \]

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