There are 1 questions in this calculation: for each question, the 3 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ third\ derivative\ of\ function\ ln(36x + e^{-5x})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( ln(36x + e^{-5x})\right)}{dx}\\=&\frac{(36 + e^{-5x}*-5)}{(36x + e^{-5x})}\\=& - \frac{5e^{-5x}}{(36x + e^{-5x})} + \frac{36}{(36x + e^{-5x})}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( - \frac{5e^{-5x}}{(36x + e^{-5x})} + \frac{36}{(36x + e^{-5x})}\right)}{dx}\\=& - 5(\frac{-(36 + e^{-5x}*-5)}{(36x + e^{-5x})^{2}})e^{-5x} - \frac{5e^{-5x}*-5}{(36x + e^{-5x})} + 36(\frac{-(36 + e^{-5x}*-5)}{(36x + e^{-5x})^{2}})\\=& - \frac{25e^{{-5x}*{2}}}{(36x + e^{-5x})^{2}} + \frac{360e^{-5x}}{(36x + e^{-5x})^{2}} + \frac{25e^{-5x}}{(36x + e^{-5x})} - \frac{1296}{(36x + e^{-5x})^{2}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( - \frac{25e^{{-5x}*{2}}}{(36x + e^{-5x})^{2}} + \frac{360e^{-5x}}{(36x + e^{-5x})^{2}} + \frac{25e^{-5x}}{(36x + e^{-5x})} - \frac{1296}{(36x + e^{-5x})^{2}}\right)}{dx}\\=& - 25(\frac{-2(36 + e^{-5x}*-5)}{(36x + e^{-5x})^{3}})e^{{-5x}*{2}} - \frac{25*2e^{-5x}e^{-5x}*-5}{(36x + e^{-5x})^{2}} + 360(\frac{-2(36 + e^{-5x}*-5)}{(36x + e^{-5x})^{3}})e^{-5x} + \frac{360e^{-5x}*-5}{(36x + e^{-5x})^{2}} + 25(\frac{-(36 + e^{-5x}*-5)}{(36x + e^{-5x})^{2}})e^{-5x} + \frac{25e^{-5x}*-5}{(36x + e^{-5x})} - 1296(\frac{-2(36 + e^{-5x}*-5)}{(36x + e^{-5x})^{3}})\\=& - \frac{250e^{{-5x}*{3}}}{(36x + e^{-5x})^{3}} + \frac{5400e^{{-5x}*{2}}}{(36x + e^{-5x})^{3}} + \frac{375e^{{-5x}*{2}}}{(36x + e^{-5x})^{2}} - \frac{38880e^{-5x}}{(36x + e^{-5x})^{3}} - \frac{2700e^{-5x}}{(36x + e^{-5x})^{2}} - \frac{125e^{-5x}}{(36x + e^{-5x})} + \frac{93312}{(36x + e^{-5x})^{3}}\\ \end{split}\end{equation} \]

Your problem has not been solved here? Please take a look at the  hot problems ！