There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ ln(24x + e^{-5x})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( ln(24x + e^{-5x})\right)}{dx}\\=&\frac{(24 + e^{-5x}*-5)}{(24x + e^{-5x})}\\=& - \frac{5e^{-5x}}{(24x + e^{-5x})} + \frac{24}{(24x + e^{-5x})}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( - \frac{5e^{-5x}}{(24x + e^{-5x})} + \frac{24}{(24x + e^{-5x})}\right)}{dx}\\=& - 5(\frac{-(24 + e^{-5x}*-5)}{(24x + e^{-5x})^{2}})e^{-5x} - \frac{5e^{-5x}*-5}{(24x + e^{-5x})} + 24(\frac{-(24 + e^{-5x}*-5)}{(24x + e^{-5x})^{2}})\\=& - \frac{25e^{{-5x}*{2}}}{(24x + e^{-5x})^{2}} + \frac{240e^{-5x}}{(24x + e^{-5x})^{2}} + \frac{25e^{-5x}}{(24x + e^{-5x})} - \frac{576}{(24x + e^{-5x})^{2}}\\ \end{split}\end{equation} \]

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