There are 1 questions in this calculation: for each question, the 3 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ third\ derivative\ of\ function\ ln(-36x + {e}^{(-x)})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( ln(-36x + {e}^{(-x)})\right)}{dx}\\=&\frac{(-36 + ({e}^{(-x)}((-1)ln(e) + \frac{(-x)(0)}{(e)})))}{(-36x + {e}^{(-x)})}\\=&\frac{-{e}^{(-x)}}{(-36x + {e}^{(-x)})} - \frac{36}{(-36x + {e}^{(-x)})}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-{e}^{(-x)}}{(-36x + {e}^{(-x)})} - \frac{36}{(-36x + {e}^{(-x)})}\right)}{dx}\\=&-(\frac{-(-36 + ({e}^{(-x)}((-1)ln(e) + \frac{(-x)(0)}{(e)})))}{(-36x + {e}^{(-x)})^{2}}){e}^{(-x)} - \frac{({e}^{(-x)}((-1)ln(e) + \frac{(-x)(0)}{(e)}))}{(-36x + {e}^{(-x)})} - 36(\frac{-(-36 + ({e}^{(-x)}((-1)ln(e) + \frac{(-x)(0)}{(e)})))}{(-36x + {e}^{(-x)})^{2}})\\=&\frac{-{e}^{(-2x)}}{(-36x + {e}^{(-x)})^{2}} - \frac{72{e}^{(-x)}}{(-36x + {e}^{(-x)})^{2}} + \frac{{e}^{(-x)}}{(-36x + {e}^{(-x)})} - \frac{1296}{(-36x + {e}^{(-x)})^{2}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{-{e}^{(-2x)}}{(-36x + {e}^{(-x)})^{2}} - \frac{72{e}^{(-x)}}{(-36x + {e}^{(-x)})^{2}} + \frac{{e}^{(-x)}}{(-36x + {e}^{(-x)})} - \frac{1296}{(-36x + {e}^{(-x)})^{2}}\right)}{dx}\\=&-(\frac{-2(-36 + ({e}^{(-x)}((-1)ln(e) + \frac{(-x)(0)}{(e)})))}{(-36x + {e}^{(-x)})^{3}}){e}^{(-2x)} - \frac{({e}^{(-2x)}((-2)ln(e) + \frac{(-2x)(0)}{(e)}))}{(-36x + {e}^{(-x)})^{2}} - 72(\frac{-2(-36 + ({e}^{(-x)}((-1)ln(e) + \frac{(-x)(0)}{(e)})))}{(-36x + {e}^{(-x)})^{3}}){e}^{(-x)} - \frac{72({e}^{(-x)}((-1)ln(e) + \frac{(-x)(0)}{(e)}))}{(-36x + {e}^{(-x)})^{2}} + (\frac{-(-36 + ({e}^{(-x)}((-1)ln(e) + \frac{(-x)(0)}{(e)})))}{(-36x + {e}^{(-x)})^{2}}){e}^{(-x)} + \frac{({e}^{(-x)}((-1)ln(e) + \frac{(-x)(0)}{(e)}))}{(-36x + {e}^{(-x)})} - 1296(\frac{-2(-36 + ({e}^{(-x)}((-1)ln(e) + \frac{(-x)(0)}{(e)})))}{(-36x + {e}^{(-x)})^{3}})\\=&\frac{-2{e}^{(-3x)}}{(-36x + {e}^{(-x)})^{3}} - \frac{216{e}^{(-2x)}}{(-36x + {e}^{(-x)})^{3}} + \frac{3{e}^{(-2x)}}{(-36x + {e}^{(-x)})^{2}} - \frac{7776{e}^{(-x)}}{(-36x + {e}^{(-x)})^{3}} + \frac{108{e}^{(-x)}}{(-36x + {e}^{(-x)})^{2}} - \frac{{e}^{(-x)}}{(-36x + {e}^{(-x)})} - \frac{93312}{(-36x + {e}^{(-x)})^{3}}\\ \end{split}\end{equation} \]

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