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

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