There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ arctan({(1 + x)}^{2})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = arctan(x^{2} + 2x + 1)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( arctan(x^{2} + 2x + 1)\right)}{dx}\\=&(\frac{(2x + 2 + 0)}{(1 + (x^{2} + 2x + 1)^{2})})\\=&\frac{2x}{(x^{4} + 4x^{3} + 6x^{2} + 4x + 2)} + \frac{2}{(x^{4} + 4x^{3} + 6x^{2} + 4x + 2)}\\ \end{split}\end{equation} \]

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