There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ \frac{x}{(a{x}^{3} + 10)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{x}{(ax^{3} + 10)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{x}{(ax^{3} + 10)}\right)}{dx}\\=&(\frac{-(a*3x^{2} + 0)}{(ax^{3} + 10)^{2}})x + \frac{1}{(ax^{3} + 10)}\\=&\frac{-3ax^{3}}{(ax^{3} + 10)^{2}} + \frac{1}{(ax^{3} + 10)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-3ax^{3}}{(ax^{3} + 10)^{2}} + \frac{1}{(ax^{3} + 10)}\right)}{dx}\\=&-3(\frac{-2(a*3x^{2} + 0)}{(ax^{3} + 10)^{3}})ax^{3} - \frac{3a*3x^{2}}{(ax^{3} + 10)^{2}} + (\frac{-(a*3x^{2} + 0)}{(ax^{3} + 10)^{2}})\\=&\frac{18a^{2}x^{5}}{(ax^{3} + 10)^{3}} - \frac{12ax^{2}}{(ax^{3} + 10)^{2}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{18a^{2}x^{5}}{(ax^{3} + 10)^{3}} - \frac{12ax^{2}}{(ax^{3} + 10)^{2}}\right)}{dx}\\=&18(\frac{-3(a*3x^{2} + 0)}{(ax^{3} + 10)^{4}})a^{2}x^{5} + \frac{18a^{2}*5x^{4}}{(ax^{3} + 10)^{3}} - 12(\frac{-2(a*3x^{2} + 0)}{(ax^{3} + 10)^{3}})ax^{2} - \frac{12a*2x}{(ax^{3} + 10)^{2}}\\=&\frac{-162a^{3}x^{7}}{(ax^{3} + 10)^{4}} + \frac{162a^{2}x^{4}}{(ax^{3} + 10)^{3}} - \frac{24ax}{(ax^{3} + 10)^{2}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{-162a^{3}x^{7}}{(ax^{3} + 10)^{4}} + \frac{162a^{2}x^{4}}{(ax^{3} + 10)^{3}} - \frac{24ax}{(ax^{3} + 10)^{2}}\right)}{dx}\\=&-162(\frac{-4(a*3x^{2} + 0)}{(ax^{3} + 10)^{5}})a^{3}x^{7} - \frac{162a^{3}*7x^{6}}{(ax^{3} + 10)^{4}} + 162(\frac{-3(a*3x^{2} + 0)}{(ax^{3} + 10)^{4}})a^{2}x^{4} + \frac{162a^{2}*4x^{3}}{(ax^{3} + 10)^{3}} - 24(\frac{-2(a*3x^{2} + 0)}{(ax^{3} + 10)^{3}})ax - \frac{24a}{(ax^{3} + 10)^{2}}\\=&\frac{1944a^{4}x^{9}}{(ax^{3} + 10)^{5}} - \frac{2592a^{3}x^{6}}{(ax^{3} + 10)^{4}} + \frac{792a^{2}x^{3}}{(ax^{3} + 10)^{3}} - \frac{24a}{(ax^{3} + 10)^{2}}\\ \end{split}\end{equation} \]

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