There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ e^{\frac{x}{(x + 2)}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = e^{\frac{x}{(x + 2)}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( e^{\frac{x}{(x + 2)}}\right)}{dx}\\=&e^{\frac{x}{(x + 2)}}((\frac{-(1 + 0)}{(x + 2)^{2}})x + \frac{1}{(x + 2)})\\=&\frac{-xe^{\frac{x}{(x + 2)}}}{(x + 2)^{2}} + \frac{e^{\frac{x}{(x + 2)}}}{(x + 2)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-xe^{\frac{x}{(x + 2)}}}{(x + 2)^{2}} + \frac{e^{\frac{x}{(x + 2)}}}{(x + 2)}\right)}{dx}\\=&-(\frac{-2(1 + 0)}{(x + 2)^{3}})xe^{\frac{x}{(x + 2)}} - \frac{e^{\frac{x}{(x + 2)}}}{(x + 2)^{2}} - \frac{xe^{\frac{x}{(x + 2)}}((\frac{-(1 + 0)}{(x + 2)^{2}})x + \frac{1}{(x + 2)})}{(x + 2)^{2}} + (\frac{-(1 + 0)}{(x + 2)^{2}})e^{\frac{x}{(x + 2)}} + \frac{e^{\frac{x}{(x + 2)}}((\frac{-(1 + 0)}{(x + 2)^{2}})x + \frac{1}{(x + 2)})}{(x + 2)}\\=& - \frac{e^{\frac{x}{(x + 2)}}}{(x + 2)^{2}} + \frac{x^{2}e^{\frac{x}{(x + 2)}}}{(x + 2)^{4}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( - \frac{e^{\frac{x}{(x + 2)}}}{(x + 2)^{2}} + \frac{x^{2}e^{\frac{x}{(x + 2)}}}{(x + 2)^{4}}\right)}{dx}\\=& - (\frac{-2(1 + 0)}{(x + 2)^{3}})e^{\frac{x}{(x + 2)}} - \frac{e^{\frac{x}{(x + 2)}}((\frac{-(1 + 0)}{(x + 2)^{2}})x + \frac{1}{(x + 2)})}{(x + 2)^{2}} + (\frac{-4(1 + 0)}{(x + 2)^{5}})x^{2}e^{\frac{x}{(x + 2)}} + \frac{2xe^{\frac{x}{(x + 2)}}}{(x + 2)^{4}} + \frac{x^{2}e^{\frac{x}{(x + 2)}}((\frac{-(1 + 0)}{(x + 2)^{2}})x + \frac{1}{(x + 2)})}{(x + 2)^{4}}\\=&\frac{e^{\frac{x}{(x + 2)}}}{(x + 2)^{3}} + \frac{3xe^{\frac{x}{(x + 2)}}}{(x + 2)^{4}} - \frac{3x^{2}e^{\frac{x}{(x + 2)}}}{(x + 2)^{5}} - \frac{x^{3}e^{\frac{x}{(x + 2)}}}{(x + 2)^{6}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{e^{\frac{x}{(x + 2)}}}{(x + 2)^{3}} + \frac{3xe^{\frac{x}{(x + 2)}}}{(x + 2)^{4}} - \frac{3x^{2}e^{\frac{x}{(x + 2)}}}{(x + 2)^{5}} - \frac{x^{3}e^{\frac{x}{(x + 2)}}}{(x + 2)^{6}}\right)}{dx}\\=&(\frac{-3(1 + 0)}{(x + 2)^{4}})e^{\frac{x}{(x + 2)}} + \frac{e^{\frac{x}{(x + 2)}}((\frac{-(1 + 0)}{(x + 2)^{2}})x + \frac{1}{(x + 2)})}{(x + 2)^{3}} + 3(\frac{-4(1 + 0)}{(x + 2)^{5}})xe^{\frac{x}{(x + 2)}} + \frac{3e^{\frac{x}{(x + 2)}}}{(x + 2)^{4}} + \frac{3xe^{\frac{x}{(x + 2)}}((\frac{-(1 + 0)}{(x + 2)^{2}})x + \frac{1}{(x + 2)})}{(x + 2)^{4}} - 3(\frac{-5(1 + 0)}{(x + 2)^{6}})x^{2}e^{\frac{x}{(x + 2)}} - \frac{3*2xe^{\frac{x}{(x + 2)}}}{(x + 2)^{5}} - \frac{3x^{2}e^{\frac{x}{(x + 2)}}((\frac{-(1 + 0)}{(x + 2)^{2}})x + \frac{1}{(x + 2)})}{(x + 2)^{5}} - (\frac{-6(1 + 0)}{(x + 2)^{7}})x^{3}e^{\frac{x}{(x + 2)}} - \frac{3x^{2}e^{\frac{x}{(x + 2)}}}{(x + 2)^{6}} - \frac{x^{3}e^{\frac{x}{(x + 2)}}((\frac{-(1 + 0)}{(x + 2)^{2}})x + \frac{1}{(x + 2)})}{(x + 2)^{6}}\\=&\frac{e^{\frac{x}{(x + 2)}}}{(x + 2)^{4}} - \frac{16xe^{\frac{x}{(x + 2)}}}{(x + 2)^{5}} + \frac{6x^{2}e^{\frac{x}{(x + 2)}}}{(x + 2)^{6}} + \frac{8x^{3}e^{\frac{x}{(x + 2)}}}{(x + 2)^{7}} + \frac{x^{4}e^{\frac{x}{(x + 2)}}}{(x + 2)^{8}}\\ \end{split}\end{equation} \]

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