There are 1 questions in this calculation: for each question, the 3 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ third\ derivative\ of\ function\ ln(-24x + {e}^{(5x)})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \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)ln(e) + \frac{(5x)(0)}{(e)})))}{(-24x + {e}^{(5x)})}\\=&\frac{5{e}^{(5x)}}{(-24x + {e}^{(5x)})} - \frac{24}{(-24x + {e}^{(5x)})}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{5{e}^{(5x)}}{(-24x + {e}^{(5x)})} - \frac{24}{(-24x + {e}^{(5x)})}\right)}{dx}\\=&5(\frac{-(-24 + ({e}^{(5x)}((5)ln(e) + \frac{(5x)(0)}{(e)})))}{(-24x + {e}^{(5x)})^{2}}){e}^{(5x)} + \frac{5({e}^{(5x)}((5)ln(e) + \frac{(5x)(0)}{(e)}))}{(-24x + {e}^{(5x)})} - 24(\frac{-(-24 + ({e}^{(5x)}((5)ln(e) + \frac{(5x)(0)}{(e)})))}{(-24x + {e}^{(5x)})^{2}})\\=&\frac{-25{e}^{(10x)}}{(-24x + {e}^{(5x)})^{2}} + \frac{240{e}^{(5x)}}{(-24x + {e}^{(5x)})^{2}} + \frac{25{e}^{(5x)}}{(-24x + {e}^{(5x)})} - \frac{576}{(-24x + {e}^{(5x)})^{2}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{-25{e}^{(10x)}}{(-24x + {e}^{(5x)})^{2}} + \frac{240{e}^{(5x)}}{(-24x + {e}^{(5x)})^{2}} + \frac{25{e}^{(5x)}}{(-24x + {e}^{(5x)})} - \frac{576}{(-24x + {e}^{(5x)})^{2}}\right)}{dx}\\=&-25(\frac{-2(-24 + ({e}^{(5x)}((5)ln(e) + \frac{(5x)(0)}{(e)})))}{(-24x + {e}^{(5x)})^{3}}){e}^{(10x)} - \frac{25({e}^{(10x)}((10)ln(e) + \frac{(10x)(0)}{(e)}))}{(-24x + {e}^{(5x)})^{2}} + 240(\frac{-2(-24 + ({e}^{(5x)}((5)ln(e) + \frac{(5x)(0)}{(e)})))}{(-24x + {e}^{(5x)})^{3}}){e}^{(5x)} + \frac{240({e}^{(5x)}((5)ln(e) + \frac{(5x)(0)}{(e)}))}{(-24x + {e}^{(5x)})^{2}} + 25(\frac{-(-24 + ({e}^{(5x)}((5)ln(e) + \frac{(5x)(0)}{(e)})))}{(-24x + {e}^{(5x)})^{2}}){e}^{(5x)} + \frac{25({e}^{(5x)}((5)ln(e) + \frac{(5x)(0)}{(e)}))}{(-24x + {e}^{(5x)})} - 576(\frac{-2(-24 + ({e}^{(5x)}((5)ln(e) + \frac{(5x)(0)}{(e)})))}{(-24x + {e}^{(5x)})^{3}})\\=&\frac{250{e}^{(15x)}}{(-24x + {e}^{(5x)})^{3}} - \frac{3600{e}^{(10x)}}{(-24x + {e}^{(5x)})^{3}} - \frac{375{e}^{(10x)}}{(-24x + {e}^{(5x)})^{2}} + \frac{17280{e}^{(5x)}}{(-24x + {e}^{(5x)})^{3}} + \frac{1800{e}^{(5x)}}{(-24x + {e}^{(5x)})^{2}} + \frac{125{e}^{(5x)}}{(-24x + {e}^{(5x)})} - \frac{27648}{(-24x + {e}^{(5x)})^{3}}\\ \end{split}\end{equation} \]

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