There are 1 questions in this calculation: for each question, the 3 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ third\ derivative\ of\ function\ 10log_{10}^{\frac{1}{x}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 10log_{10}^{\frac{1}{x}}\right)}{dx}\\=&10(\frac{(\frac{(\frac{-1}{x^{2}})}{(\frac{1}{x})} - \frac{(0)log_{10}^{\frac{1}{x}}}{(10)})}{(ln(10))})\\=&\frac{-10}{xln(10)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-10}{xln(10)}\right)}{dx}\\=&\frac{-10*-1}{x^{2}ln(10)} - \frac{10*-0}{xln^{2}(10)(10)}\\=&\frac{10}{x^{2}ln(10)}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{10}{x^{2}ln(10)}\right)}{dx}\\=&\frac{10*-2}{x^{3}ln(10)} + \frac{10*-0}{x^{2}ln^{2}(10)(10)}\\=&\frac{-20}{x^{3}ln(10)}\\ \end{split}\end{equation} \]

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