There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ e^{e^{lg(x)}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( e^{e^{lg(x)}}\right)}{dx}\\=&\frac{e^{e^{lg(x)}}e^{lg(x)}}{ln{10}(x)}\\=&\frac{e^{e^{lg(x)}}e^{lg(x)}}{xln{10}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{e^{e^{lg(x)}}e^{lg(x)}}{xln{10}}\right)}{dx}\\=&\frac{-e^{e^{lg(x)}}e^{lg(x)}}{x^{2}ln{10}} + \frac{e^{e^{lg(x)}}e^{lg(x)}e^{lg(x)}}{xln{10}(x)ln{10}} + \frac{e^{e^{lg(x)}}e^{lg(x)}}{xln{10}(x)ln{10}} + \frac{e^{e^{lg(x)}}e^{lg(x)}*-0}{xln^{2}{10}}\\=&\frac{-e^{e^{lg(x)}}e^{lg(x)}}{x^{2}ln{10}} + \frac{e^{e^{lg(x)}}e^{{lg(x)}*{2}}}{x^{2}ln^{2}{10}} + \frac{e^{e^{lg(x)}}e^{lg(x)}}{x^{2}ln^{2}{10}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{-e^{e^{lg(x)}}e^{lg(x)}}{x^{2}ln{10}} + \frac{e^{e^{lg(x)}}e^{{lg(x)}*{2}}}{x^{2}ln^{2}{10}} + \frac{e^{e^{lg(x)}}e^{lg(x)}}{x^{2}ln^{2}{10}}\right)}{dx}\\=&\frac{--2e^{e^{lg(x)}}e^{lg(x)}}{x^{3}ln{10}} - \frac{e^{e^{lg(x)}}e^{lg(x)}e^{lg(x)}}{x^{2}ln{10}(x)ln{10}} - \frac{e^{e^{lg(x)}}e^{lg(x)}}{x^{2}ln{10}(x)ln{10}} - \frac{e^{e^{lg(x)}}e^{lg(x)}*-0}{x^{2}ln^{2}{10}} + \frac{-2e^{e^{lg(x)}}e^{{lg(x)}*{2}}}{x^{3}ln^{2}{10}} + \frac{e^{e^{lg(x)}}e^{lg(x)}e^{{lg(x)}*{2}}}{x^{2}ln{10}(x)ln^{2}{10}} + \frac{e^{e^{lg(x)}}*2e^{lg(x)}e^{lg(x)}}{x^{2}ln{10}(x)ln^{2}{10}} + \frac{e^{e^{lg(x)}}e^{{lg(x)}*{2}}*-2*0}{x^{2}ln^{3}{10}} + \frac{-2e^{e^{lg(x)}}e^{lg(x)}}{x^{3}ln^{2}{10}} + \frac{e^{e^{lg(x)}}e^{lg(x)}e^{lg(x)}}{x^{2}ln{10}(x)ln^{2}{10}} + \frac{e^{e^{lg(x)}}e^{lg(x)}}{x^{2}ln{10}(x)ln^{2}{10}} + \frac{e^{e^{lg(x)}}e^{lg(x)}*-2*0}{x^{2}ln^{3}{10}}\\=&\frac{2e^{e^{lg(x)}}e^{lg(x)}}{x^{3}ln{10}} - \frac{3e^{e^{lg(x)}}e^{{lg(x)}*{2}}}{x^{3}ln^{2}{10}} - \frac{3e^{e^{lg(x)}}e^{lg(x)}}{x^{3}ln^{2}{10}} + \frac{e^{e^{lg(x)}}e^{{lg(x)}*{3}}}{x^{3}ln^{3}{10}} + \frac{2e^{{lg(x)}*{2}}e^{e^{lg(x)}}}{x^{3}ln^{3}{10}} + \frac{e^{e^{lg(x)}}e^{{lg(x)}*{2}}}{x^{3}ln^{3}{10}} + \frac{e^{e^{lg(x)}}e^{lg(x)}}{x^{3}ln^{3}{10}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{2e^{e^{lg(x)}}e^{lg(x)}}{x^{3}ln{10}} - \frac{3e^{e^{lg(x)}}e^{{lg(x)}*{2}}}{x^{3}ln^{2}{10}} - \frac{3e^{e^{lg(x)}}e^{lg(x)}}{x^{3}ln^{2}{10}} + \frac{e^{e^{lg(x)}}e^{{lg(x)}*{3}}}{x^{3}ln^{3}{10}} + \frac{2e^{{lg(x)}*{2}}e^{e^{lg(x)}}}{x^{3}ln^{3}{10}} + \frac{e^{e^{lg(x)}}e^{{lg(x)}*{2}}}{x^{3}ln^{3}{10}} + \frac{e^{e^{lg(x)}}e^{lg(x)}}{x^{3}ln^{3}{10}}\right)}{dx}\\=&\frac{2*-3e^{e^{lg(x)}}e^{lg(x)}}{x^{4}ln{10}} + \frac{2e^{e^{lg(x)}}e^{lg(x)}e^{lg(x)}}{x^{3}ln{10}(x)ln{10}} + \frac{2e^{e^{lg(x)}}e^{lg(x)}}{x^{3}ln{10}(x)ln{10}} + \frac{2e^{e^{lg(x)}}e^{lg(x)}*-0}{x^{3}ln^{2}{10}} - \frac{3*-3e^{e^{lg(x)}}e^{{lg(x)}*{2}}}{x^{4}ln^{2}{10}} - \frac{3e^{e^{lg(x)}}e^{lg(x)}e^{{lg(x)}*{2}}}{x^{3}ln{10}(x)ln^{2}{10}} - \frac{3e^{e^{lg(x)}}*2e^{lg(x)}e^{lg(x)}}{x^{3}ln{10}(x)ln^{2}{10}} - \frac{3e^{e^{lg(x)}}e^{{lg(x)}*{2}}*-2*0}{x^{3}ln^{3}{10}} - \frac{3*-3e^{e^{lg(x)}}e^{lg(x)}}{x^{4}ln^{2}{10}} - \frac{3e^{e^{lg(x)}}e^{lg(x)}e^{lg(x)}}{x^{3}ln{10}(x)ln^{2}{10}} - \frac{3e^{e^{lg(x)}}e^{lg(x)}}{x^{3}ln{10}(x)ln^{2}{10}} - \frac{3e^{e^{lg(x)}}e^{lg(x)}*-2*0}{x^{3}ln^{3}{10}} + \frac{-3e^{e^{lg(x)}}e^{{lg(x)}*{3}}}{x^{4}ln^{3}{10}} + \frac{e^{e^{lg(x)}}e^{lg(x)}e^{{lg(x)}*{3}}}{x^{3}ln{10}(x)ln^{3}{10}} + \frac{e^{e^{lg(x)}}*3e^{{lg(x)}*{2}}e^{lg(x)}}{x^{3}ln{10}(x)ln^{3}{10}} + \frac{e^{e^{lg(x)}}e^{{lg(x)}*{3}}*-3*0}{x^{3}ln^{4}{10}} + \frac{2*-3e^{{lg(x)}*{2}}e^{e^{lg(x)}}}{x^{4}ln^{3}{10}} + \frac{2*2e^{lg(x)}e^{lg(x)}e^{e^{lg(x)}}}{x^{3}ln{10}(x)ln^{3}{10}} + \frac{2e^{{lg(x)}*{2}}e^{e^{lg(x)}}e^{lg(x)}}{x^{3}ln{10}(x)ln^{3}{10}} + \frac{2e^{{lg(x)}*{2}}e^{e^{lg(x)}}*-3*0}{x^{3}ln^{4}{10}} + \frac{-3e^{e^{lg(x)}}e^{{lg(x)}*{2}}}{x^{4}ln^{3}{10}} + \frac{e^{e^{lg(x)}}e^{lg(x)}e^{{lg(x)}*{2}}}{x^{3}ln{10}(x)ln^{3}{10}} + \frac{e^{e^{lg(x)}}*2e^{lg(x)}e^{lg(x)}}{x^{3}ln{10}(x)ln^{3}{10}} + \frac{e^{e^{lg(x)}}e^{{lg(x)}*{2}}*-3*0}{x^{3}ln^{4}{10}} + \frac{-3e^{e^{lg(x)}}e^{lg(x)}}{x^{4}ln^{3}{10}} + \frac{e^{e^{lg(x)}}e^{lg(x)}e^{lg(x)}}{x^{3}ln{10}(x)ln^{3}{10}} + \frac{e^{e^{lg(x)}}e^{lg(x)}}{x^{3}ln{10}(x)ln^{3}{10}} + \frac{e^{e^{lg(x)}}e^{lg(x)}*-3*0}{x^{3}ln^{4}{10}}\\=&\frac{-6e^{e^{lg(x)}}e^{lg(x)}}{x^{4}ln{10}} + \frac{11e^{e^{lg(x)}}e^{{lg(x)}*{2}}}{x^{4}ln^{2}{10}} + \frac{11e^{e^{lg(x)}}e^{lg(x)}}{x^{4}ln^{2}{10}} - \frac{6e^{e^{lg(x)}}e^{{lg(x)}*{3}}}{x^{4}ln^{3}{10}} - \frac{12e^{{lg(x)}*{2}}e^{e^{lg(x)}}}{x^{4}ln^{3}{10}} - \frac{6e^{e^{lg(x)}}e^{{lg(x)}*{2}}}{x^{4}ln^{3}{10}} - \frac{6e^{e^{lg(x)}}e^{lg(x)}}{x^{4}ln^{3}{10}} + \frac{e^{e^{lg(x)}}e^{{lg(x)}*{4}}}{x^{4}ln^{4}{10}} + \frac{5e^{{lg(x)}*{3}}e^{e^{lg(x)}}}{x^{4}ln^{4}{10}} + \frac{6e^{{lg(x)}*{2}}e^{e^{lg(x)}}}{x^{4}ln^{4}{10}} + \frac{e^{e^{lg(x)}}e^{{lg(x)}*{3}}}{x^{4}ln^{4}{10}} + \frac{e^{e^{lg(x)}}e^{{lg(x)}*{2}}}{x^{4}ln^{4}{10}} + \frac{e^{e^{lg(x)}}e^{lg(x)}}{x^{4}ln^{4}{10}}\\ \end{split}\end{equation} \]

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