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

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