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

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