There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(3{x}^{2} + {x}^{3})}{(2{(1 + x)}^{3})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{\frac{3}{2}x^{2}}{(x + 1)^{3}} + \frac{\frac{1}{2}x^{3}}{(x + 1)^{3}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{\frac{3}{2}x^{2}}{(x + 1)^{3}} + \frac{\frac{1}{2}x^{3}}{(x + 1)^{3}}\right)}{dx}\\=&\frac{3}{2}(\frac{-3(1 + 0)}{(x + 1)^{4}})x^{2} + \frac{\frac{3}{2}*2x}{(x + 1)^{3}} + \frac{1}{2}(\frac{-3(1 + 0)}{(x + 1)^{4}})x^{3} + \frac{\frac{1}{2}*3x^{2}}{(x + 1)^{3}}\\=&\frac{-9x^{2}}{2(x + 1)^{4}} + \frac{3x}{(x + 1)^{3}} - \frac{3x^{3}}{2(x + 1)^{4}} + \frac{3x^{2}}{2(x + 1)^{3}}\\ \end{split}\end{equation} \]

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