There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ ln(12x + {e}^{x})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( ln(12x + {e}^{x})\right)}{dx}\\=&\frac{(12 + ({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)})))}{(12x + {e}^{x})}\\=&\frac{{e}^{x}}{(12x + {e}^{x})} + \frac{12}{(12x + {e}^{x})}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{{e}^{x}}{(12x + {e}^{x})} + \frac{12}{(12x + {e}^{x})}\right)}{dx}\\=&(\frac{-(12 + ({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)})))}{(12x + {e}^{x})^{2}}){e}^{x} + \frac{({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))}{(12x + {e}^{x})} + 12(\frac{-(12 + ({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)})))}{(12x + {e}^{x})^{2}})\\=&\frac{-{e}^{(2x)}}{(12x + {e}^{x})^{2}} - \frac{24{e}^{x}}{(12x + {e}^{x})^{2}} + \frac{{e}^{x}}{(12x + {e}^{x})} - \frac{144}{(12x + {e}^{x})^{2}}\\ \end{split}\end{equation} \]

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