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

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