There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ ln(ln(ln(x))) - xsin(x)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( ln(ln(ln(x))) - xsin(x)\right)}{dx}\\=&\frac{1}{(ln(ln(x)))(ln(x))(x)} - sin(x) - xcos(x)\\=&\frac{1}{xln(ln(x))ln(x)} - sin(x) - xcos(x)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{1}{xln(ln(x))ln(x)} - sin(x) - xcos(x)\right)}{dx}\\=&\frac{-1}{x^{2}ln(ln(x))ln(x)} + \frac{-1}{xln^{2}(ln(x))(ln(x))(x)ln(x)} + \frac{-1}{xln(ln(x))ln^{2}(x)(x)} - cos(x) - cos(x) - x*-sin(x)\\=&\frac{-1}{x^{2}ln(ln(x))ln(x)} - \frac{1}{x^{2}ln^{2}(ln(x))ln^{2}(x)} - \frac{1}{x^{2}ln^{2}(x)ln(ln(x))} - 2cos(x) + xsin(x)\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{-1}{x^{2}ln(ln(x))ln(x)} - \frac{1}{x^{2}ln^{2}(ln(x))ln^{2}(x)} - \frac{1}{x^{2}ln^{2}(x)ln(ln(x))} - 2cos(x) + xsin(x)\right)}{dx}\\=&\frac{--2}{x^{3}ln(ln(x))ln(x)} - \frac{-1}{x^{2}ln^{2}(ln(x))(ln(x))(x)ln(x)} - \frac{-1}{x^{2}ln(ln(x))ln^{2}(x)(x)} - \frac{-2}{x^{3}ln^{2}(ln(x))ln^{2}(x)} - \frac{-2}{x^{2}ln^{3}(ln(x))(ln(x))(x)ln^{2}(x)} - \frac{-2}{x^{2}ln^{2}(ln(x))ln^{3}(x)(x)} - \frac{-2}{x^{3}ln^{2}(x)ln(ln(x))} - \frac{-2}{x^{2}ln^{3}(x)(x)ln(ln(x))} - \frac{-1}{x^{2}ln^{2}(x)ln^{2}(ln(x))(ln(x))(x)} - 2*-sin(x) + sin(x) + xcos(x)\\=&\frac{2}{x^{3}ln(ln(x))ln(x)} + \frac{3}{x^{3}ln^{2}(ln(x))ln^{2}(x)} + \frac{3}{x^{3}ln^{2}(x)ln(ln(x))} + \frac{2}{x^{3}ln^{3}(ln(x))ln^{3}(x)} + \frac{3}{x^{3}ln^{3}(x)ln^{2}(ln(x))} + \frac{2}{x^{3}ln^{3}(x)ln(ln(x))} + 3sin(x) + xcos(x)\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{2}{x^{3}ln(ln(x))ln(x)} + \frac{3}{x^{3}ln^{2}(ln(x))ln^{2}(x)} + \frac{3}{x^{3}ln^{2}(x)ln(ln(x))} + \frac{2}{x^{3}ln^{3}(ln(x))ln^{3}(x)} + \frac{3}{x^{3}ln^{3}(x)ln^{2}(ln(x))} + \frac{2}{x^{3}ln^{3}(x)ln(ln(x))} + 3sin(x) + xcos(x)\right)}{dx}\\=&\frac{2*-3}{x^{4}ln(ln(x))ln(x)} + \frac{2*-1}{x^{3}ln^{2}(ln(x))(ln(x))(x)ln(x)} + \frac{2*-1}{x^{3}ln(ln(x))ln^{2}(x)(x)} + \frac{3*-3}{x^{4}ln^{2}(ln(x))ln^{2}(x)} + \frac{3*-2}{x^{3}ln^{3}(ln(x))(ln(x))(x)ln^{2}(x)} + \frac{3*-2}{x^{3}ln^{2}(ln(x))ln^{3}(x)(x)} + \frac{3*-3}{x^{4}ln^{2}(x)ln(ln(x))} + \frac{3*-2}{x^{3}ln^{3}(x)(x)ln(ln(x))} + \frac{3*-1}{x^{3}ln^{2}(x)ln^{2}(ln(x))(ln(x))(x)} + \frac{2*-3}{x^{4}ln^{3}(ln(x))ln^{3}(x)} + \frac{2*-3}{x^{3}ln^{4}(ln(x))(ln(x))(x)ln^{3}(x)} + \frac{2*-3}{x^{3}ln^{3}(ln(x))ln^{4}(x)(x)} + \frac{3*-3}{x^{4}ln^{3}(x)ln^{2}(ln(x))} + \frac{3*-3}{x^{3}ln^{4}(x)(x)ln^{2}(ln(x))} + \frac{3*-2}{x^{3}ln^{3}(x)ln^{3}(ln(x))(ln(x))(x)} + \frac{2*-3}{x^{4}ln^{3}(x)ln(ln(x))} + \frac{2*-3}{x^{3}ln^{4}(x)(x)ln(ln(x))} + \frac{2*-1}{x^{3}ln^{3}(x)ln^{2}(ln(x))(ln(x))(x)} + 3cos(x) + cos(x) + x*-sin(x)\\=&\frac{-6}{x^{4}ln(ln(x))ln(x)} - \frac{11}{x^{4}ln^{2}(ln(x))ln^{2}(x)} - \frac{11}{x^{4}ln^{2}(x)ln(ln(x))} - \frac{12}{x^{4}ln^{3}(ln(x))ln^{3}(x)} - \frac{18}{x^{4}ln^{3}(x)ln^{2}(ln(x))} - \frac{12}{x^{4}ln^{3}(x)ln(ln(x))} - \frac{6}{x^{4}ln^{4}(ln(x))ln^{4}(x)} - \frac{12}{x^{4}ln^{4}(x)ln^{3}(ln(x))} - \frac{11}{x^{4}ln^{4}(x)ln^{2}(ln(x))} - \frac{6}{x^{4}ln^{4}(x)ln(ln(x))} + 4cos(x) - xsin(x)\\ \end{split}\end{equation} \]

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