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

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