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

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