There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ log_{e^{x}}^{{10}^{x}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( log_{e^{x}}^{{10}^{x}}\right)}{dx}\\=&(\frac{(\frac{(({10}^{x}((1)ln(10) + \frac{(x)(0)}{(10)})))}{({10}^{x})} - \frac{(e^{x})log_{e^{x}}^{{10}^{x}}}{(e^{x})})}{(ln(e^{x}))})\\=&\frac{ln(10)}{ln(e^{x})} - \frac{log_{e^{x}}^{{10}^{x}}}{ln(e^{x})}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{ln(10)}{ln(e^{x})} - \frac{log_{e^{x}}^{{10}^{x}}}{ln(e^{x})}\right)}{dx}\\=&\frac{0}{(10)ln(e^{x})} + \frac{ln(10)*-e^{x}}{ln^{2}(e^{x})(e^{x})} - \frac{(\frac{(\frac{(({10}^{x}((1)ln(10) + \frac{(x)(0)}{(10)})))}{({10}^{x})} - \frac{(e^{x})log_{e^{x}}^{{10}^{x}}}{(e^{x})})}{(ln(e^{x}))})}{ln(e^{x})} - \frac{log_{e^{x}}^{{10}^{x}}*-e^{x}}{ln^{2}(e^{x})(e^{x})}\\=&\frac{-ln(10)}{ln^{2}(e^{x})} - \frac{ln(10)}{ln^{2}(e^{x})} + \frac{2log_{e^{x}}^{{10}^{x}}}{ln^{2}(e^{x})}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{-ln(10)}{ln^{2}(e^{x})} - \frac{ln(10)}{ln^{2}(e^{x})} + \frac{2log_{e^{x}}^{{10}^{x}}}{ln^{2}(e^{x})}\right)}{dx}\\=&\frac{--2e^{x}ln(10)}{ln^{3}(e^{x})(e^{x})} - \frac{0}{ln^{2}(e^{x})(10)} - \frac{0}{(10)ln^{2}(e^{x})} - \frac{ln(10)*-2e^{x}}{ln^{3}(e^{x})(e^{x})} + \frac{2(\frac{(\frac{(({10}^{x}((1)ln(10) + \frac{(x)(0)}{(10)})))}{({10}^{x})} - \frac{(e^{x})log_{e^{x}}^{{10}^{x}}}{(e^{x})})}{(ln(e^{x}))})}{ln^{2}(e^{x})} + \frac{2log_{e^{x}}^{{10}^{x}}*-2e^{x}}{ln^{3}(e^{x})(e^{x})}\\=&\frac{4ln(10)}{ln^{3}(e^{x})} + \frac{2ln(10)}{ln^{3}(e^{x})} - \frac{6log_{e^{x}}^{{10}^{x}}}{ln^{3}(e^{x})}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{4ln(10)}{ln^{3}(e^{x})} + \frac{2ln(10)}{ln^{3}(e^{x})} - \frac{6log_{e^{x}}^{{10}^{x}}}{ln^{3}(e^{x})}\right)}{dx}\\=&\frac{4*-3e^{x}ln(10)}{ln^{4}(e^{x})(e^{x})} + \frac{4*0}{ln^{3}(e^{x})(10)} + \frac{2*0}{(10)ln^{3}(e^{x})} + \frac{2ln(10)*-3e^{x}}{ln^{4}(e^{x})(e^{x})} - \frac{6(\frac{(\frac{(({10}^{x}((1)ln(10) + \frac{(x)(0)}{(10)})))}{({10}^{x})} - \frac{(e^{x})log_{e^{x}}^{{10}^{x}}}{(e^{x})})}{(ln(e^{x}))})}{ln^{3}(e^{x})} - \frac{6log_{e^{x}}^{{10}^{x}}*-3e^{x}}{ln^{4}(e^{x})(e^{x})}\\=&\frac{-18ln(10)}{ln^{4}(e^{x})} - \frac{6ln(10)}{ln^{4}(e^{x})} + \frac{24log_{e^{x}}^{{10}^{x}}}{ln^{4}(e^{x})}\\ \end{split}\end{equation} \]

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