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

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