There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ x(x - 9){(x - 9)}^{-1}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{x^{2}}{(x - 9)} - \frac{9x}{(x - 9)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{x^{2}}{(x - 9)} - \frac{9x}{(x - 9)}\right)}{dx}\\=&(\frac{-(1 + 0)}{(x - 9)^{2}})x^{2} + \frac{2x}{(x - 9)} - 9(\frac{-(1 + 0)}{(x - 9)^{2}})x - \frac{9}{(x - 9)}\\=&\frac{-x^{2}}{(x - 9)^{2}} + \frac{2x}{(x - 9)} + \frac{9x}{(x - 9)^{2}} - \frac{9}{(x - 9)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-x^{2}}{(x - 9)^{2}} + \frac{2x}{(x - 9)} + \frac{9x}{(x - 9)^{2}} - \frac{9}{(x - 9)}\right)}{dx}\\=&-(\frac{-2(1 + 0)}{(x - 9)^{3}})x^{2} - \frac{2x}{(x - 9)^{2}} + 2(\frac{-(1 + 0)}{(x - 9)^{2}})x + \frac{2}{(x - 9)} + 9(\frac{-2(1 + 0)}{(x - 9)^{3}})x + \frac{9}{(x - 9)^{2}} - 9(\frac{-(1 + 0)}{(x - 9)^{2}})\\=&\frac{2x^{2}}{(x - 9)^{3}} - \frac{4x}{(x - 9)^{2}} - \frac{18x}{(x - 9)^{3}} + \frac{18}{(x - 9)^{2}} + \frac{2}{(x - 9)}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{2x^{2}}{(x - 9)^{3}} - \frac{4x}{(x - 9)^{2}} - \frac{18x}{(x - 9)^{3}} + \frac{18}{(x - 9)^{2}} + \frac{2}{(x - 9)}\right)}{dx}\\=&2(\frac{-3(1 + 0)}{(x - 9)^{4}})x^{2} + \frac{2*2x}{(x - 9)^{3}} - 4(\frac{-2(1 + 0)}{(x - 9)^{3}})x - \frac{4}{(x - 9)^{2}} - 18(\frac{-3(1 + 0)}{(x - 9)^{4}})x - \frac{18}{(x - 9)^{3}} + 18(\frac{-2(1 + 0)}{(x - 9)^{3}}) + 2(\frac{-(1 + 0)}{(x - 9)^{2}})\\=&\frac{-6x^{2}}{(x - 9)^{4}} + \frac{12x}{(x - 9)^{3}} + \frac{54x}{(x - 9)^{4}} - \frac{54}{(x - 9)^{3}} - \frac{6}{(x - 9)^{2}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{-6x^{2}}{(x - 9)^{4}} + \frac{12x}{(x - 9)^{3}} + \frac{54x}{(x - 9)^{4}} - \frac{54}{(x - 9)^{3}} - \frac{6}{(x - 9)^{2}}\right)}{dx}\\=&-6(\frac{-4(1 + 0)}{(x - 9)^{5}})x^{2} - \frac{6*2x}{(x - 9)^{4}} + 12(\frac{-3(1 + 0)}{(x - 9)^{4}})x + \frac{12}{(x - 9)^{3}} + 54(\frac{-4(1 + 0)}{(x - 9)^{5}})x + \frac{54}{(x - 9)^{4}} - 54(\frac{-3(1 + 0)}{(x - 9)^{4}}) - 6(\frac{-2(1 + 0)}{(x - 9)^{3}})\\=&\frac{24x^{2}}{(x - 9)^{5}} - \frac{48x}{(x - 9)^{4}} - \frac{216x}{(x - 9)^{5}} + \frac{216}{(x - 9)^{4}} + \frac{24}{(x - 9)^{3}}\\ \end{split}\end{equation} \]

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