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

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