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

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