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

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