There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ e^{{\frac{1}{x}}^{2}}arctan(\frac{({x}^{2} + x + 1)(x - 2)}{(x + 1)})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = e^{\frac{1}{x^{2}}}arctan(\frac{x^{3}}{(x + 1)} - \frac{x^{2}}{(x + 1)} - \frac{x}{(x + 1)} - \frac{2}{(x + 1)})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( e^{\frac{1}{x^{2}}}arctan(\frac{x^{3}}{(x + 1)} - \frac{x^{2}}{(x + 1)} - \frac{x}{(x + 1)} - \frac{2}{(x + 1)})\right)}{dx}\\=&\frac{e^{\frac{1}{x^{2}}}*-2arctan(\frac{x^{3}}{(x + 1)} - \frac{x^{2}}{(x + 1)} - \frac{x}{(x + 1)} - \frac{2}{(x + 1)})}{x^{3}} + e^{\frac{1}{x^{2}}}(\frac{((\frac{-(1 + 0)}{(x + 1)^{2}})x^{3} + \frac{3x^{2}}{(x + 1)} - (\frac{-(1 + 0)}{(x + 1)^{2}})x^{2} - \frac{2x}{(x + 1)} - (\frac{-(1 + 0)}{(x + 1)^{2}})x - \frac{1}{(x + 1)} - 2(\frac{-(1 + 0)}{(x + 1)^{2}}))}{(1 + (\frac{x^{3}}{(x + 1)} - \frac{x^{2}}{(x + 1)} - \frac{x}{(x + 1)} - \frac{2}{(x + 1)})^{2})})\\=&\frac{-2e^{\frac{1}{x^{2}}}arctan(\frac{x^{3}}{(x + 1)} - \frac{x^{2}}{(x + 1)} - \frac{x}{(x + 1)} - \frac{2}{(x + 1)})}{x^{3}} - \frac{x^{3}e^{\frac{1}{x^{2}}}}{(x + 1)^{2}(\frac{x^{6}}{(x + 1)^{2}} - \frac{2x^{5}}{(x + 1)^{2}} - \frac{x^{4}}{(x + 1)^{2}} - \frac{2x^{3}}{(x + 1)^{2}} + \frac{5x^{2}}{(x + 1)^{2}} + \frac{4x}{(x + 1)^{2}} + \frac{4}{(x + 1)^{2}} + 1)} + \frac{3x^{2}e^{\frac{1}{x^{2}}}}{(x + 1)(\frac{x^{6}}{(x + 1)^{2}} - \frac{2x^{5}}{(x + 1)^{2}} - \frac{x^{4}}{(x + 1)^{2}} - \frac{2x^{3}}{(x + 1)^{2}} + \frac{5x^{2}}{(x + 1)^{2}} + \frac{4x}{(x + 1)^{2}} + \frac{4}{(x + 1)^{2}} + 1)} + \frac{x^{2}e^{\frac{1}{x^{2}}}}{(x + 1)^{2}(\frac{x^{6}}{(x + 1)^{2}} - \frac{2x^{5}}{(x + 1)^{2}} - \frac{x^{4}}{(x + 1)^{2}} - \frac{2x^{3}}{(x + 1)^{2}} + \frac{5x^{2}}{(x + 1)^{2}} + \frac{4x}{(x + 1)^{2}} + \frac{4}{(x + 1)^{2}} + 1)} - \frac{2xe^{\frac{1}{x^{2}}}}{(x + 1)(\frac{x^{6}}{(x + 1)^{2}} - \frac{2x^{5}}{(x + 1)^{2}} - \frac{x^{4}}{(x + 1)^{2}} - \frac{2x^{3}}{(x + 1)^{2}} + \frac{5x^{2}}{(x + 1)^{2}} + \frac{4x}{(x + 1)^{2}} + \frac{4}{(x + 1)^{2}} + 1)} + \frac{xe^{\frac{1}{x^{2}}}}{(x + 1)^{2}(\frac{x^{6}}{(x + 1)^{2}} - \frac{2x^{5}}{(x + 1)^{2}} - \frac{x^{4}}{(x + 1)^{2}} - \frac{2x^{3}}{(x + 1)^{2}} + \frac{5x^{2}}{(x + 1)^{2}} + \frac{4x}{(x + 1)^{2}} + \frac{4}{(x + 1)^{2}} + 1)} - \frac{e^{\frac{1}{x^{2}}}}{(x + 1)(\frac{x^{6}}{(x + 1)^{2}} - \frac{2x^{5}}{(x + 1)^{2}} - \frac{x^{4}}{(x + 1)^{2}} - \frac{2x^{3}}{(x + 1)^{2}} + \frac{5x^{2}}{(x + 1)^{2}} + \frac{4x}{(x + 1)^{2}} + \frac{4}{(x + 1)^{2}} + 1)} + \frac{2e^{\frac{1}{x^{2}}}}{(x + 1)^{2}(\frac{x^{6}}{(x + 1)^{2}} - \frac{2x^{5}}{(x + 1)^{2}} - \frac{x^{4}}{(x + 1)^{2}} - \frac{2x^{3}}{(x + 1)^{2}} + \frac{5x^{2}}{(x + 1)^{2}} + \frac{4x}{(x + 1)^{2}} + \frac{4}{(x + 1)^{2}} + 1)}\\ \end{split}\end{equation} \]

Your problem has not been solved here? Please take a look at the  hot problems ！