There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ ln(36x + {e}^{(2x)})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( ln(36x + {e}^{(2x)})\right)}{dx}\\=&\frac{(36 + ({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)})))}{(36x + {e}^{(2x)})}\\=&\frac{2{e}^{(2x)}}{(36x + {e}^{(2x)})} + \frac{36}{(36x + {e}^{(2x)})}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{2{e}^{(2x)}}{(36x + {e}^{(2x)})} + \frac{36}{(36x + {e}^{(2x)})}\right)}{dx}\\=&2(\frac{-(36 + ({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)})))}{(36x + {e}^{(2x)})^{2}}){e}^{(2x)} + \frac{2({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))}{(36x + {e}^{(2x)})} + 36(\frac{-(36 + ({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)})))}{(36x + {e}^{(2x)})^{2}})\\=&\frac{-4{e}^{(4x)}}{(36x + {e}^{(2x)})^{2}} - \frac{144{e}^{(2x)}}{(36x + {e}^{(2x)})^{2}} + \frac{4{e}^{(2x)}}{(36x + {e}^{(2x)})} - \frac{1296}{(36x + {e}^{(2x)})^{2}}\\ \end{split}\end{equation} \]

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