There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ ln(12x + e^{4x})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( ln(12x + e^{4x})\right)}{dx}\\=&\frac{(12 + e^{4x}*4)}{(12x + e^{4x})}\\=&\frac{4e^{4x}}{(12x + e^{4x})} + \frac{12}{(12x + e^{4x})}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{4e^{4x}}{(12x + e^{4x})} + \frac{12}{(12x + e^{4x})}\right)}{dx}\\=&4(\frac{-(12 + e^{4x}*4)}{(12x + e^{4x})^{2}})e^{4x} + \frac{4e^{4x}*4}{(12x + e^{4x})} + 12(\frac{-(12 + e^{4x}*4)}{(12x + e^{4x})^{2}})\\=& - \frac{16e^{{4x}*{2}}}{(12x + e^{4x})^{2}} - \frac{96e^{4x}}{(12x + e^{4x})^{2}} + \frac{16e^{4x}}{(12x + e^{4x})} - \frac{144}{(12x + e^{4x})^{2}}\\ \end{split}\end{equation} \]

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