There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ 2arctan({({e}^{x} - 1)}^{2})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 2arctan({e}^{(2(x))} - 2{e}^{x} + 1)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 2arctan({e}^{(2(x))} - 2{e}^{x} + 1)\right)}{dx}\\=&2(\frac{(({e}^{(2(x))}((2(1))ln(e) + \frac{(2(x))(0)}{(e)})) - 2({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)})) + 0)}{(1 + ({e}^{(2(x))} - 2{e}^{x} + 1)^{2})})\\=&\frac{4{e}^{(2x)}}{(-2{e}^{(2x)}{e}^{x} - 2{e}^{x}{e}^{(2x)} + {e}^{(4x)} + 6{e}^{(2x)} - 4{e}^{x} + 2)} - \frac{4{e}^{x}}{(-2{e}^{(2x)}{e}^{x} - 2{e}^{x}{e}^{(2x)} + {e}^{(4x)} + 6{e}^{(2x)} - 4{e}^{x} + 2)}\\ \end{split}\end{equation} \]

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