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

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