There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ ln(-24x + {e}^{(4x)})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( ln(-24x + {e}^{(4x)})\right)}{dx}\\=&\frac{(-24 + ({e}^{(4x)}((4)ln(e) + \frac{(4x)(0)}{(e)})))}{(-24x + {e}^{(4x)})}\\=&\frac{4{e}^{(4x)}}{(-24x + {e}^{(4x)})} - \frac{24}{(-24x + {e}^{(4x)})}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{4{e}^{(4x)}}{(-24x + {e}^{(4x)})} - \frac{24}{(-24x + {e}^{(4x)})}\right)}{dx}\\=&4(\frac{-(-24 + ({e}^{(4x)}((4)ln(e) + \frac{(4x)(0)}{(e)})))}{(-24x + {e}^{(4x)})^{2}}){e}^{(4x)} + \frac{4({e}^{(4x)}((4)ln(e) + \frac{(4x)(0)}{(e)}))}{(-24x + {e}^{(4x)})} - 24(\frac{-(-24 + ({e}^{(4x)}((4)ln(e) + \frac{(4x)(0)}{(e)})))}{(-24x + {e}^{(4x)})^{2}})\\=&\frac{-16{e}^{(8x)}}{(-24x + {e}^{(4x)})^{2}} + \frac{192{e}^{(4x)}}{(-24x + {e}^{(4x)})^{2}} + \frac{16{e}^{(4x)}}{(-24x + {e}^{(4x)})} - \frac{576}{(-24x + {e}^{(4x)})^{2}}\\ \end{split}\end{equation} \]

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