There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(3{x}^{2} + 4x)}{(2{(x + 1)}^{\frac{3}{2}})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{\frac{3}{2}x^{2}}{(x + 1)^{\frac{3}{2}}} + \frac{2x}{(x + 1)^{\frac{3}{2}}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{\frac{3}{2}x^{2}}{(x + 1)^{\frac{3}{2}}} + \frac{2x}{(x + 1)^{\frac{3}{2}}}\right)}{dx}\\=&\frac{3}{2}(\frac{\frac{-3}{2}(1 + 0)}{(x + 1)^{\frac{5}{2}}})x^{2} + \frac{\frac{3}{2}*2x}{(x + 1)^{\frac{3}{2}}} + 2(\frac{\frac{-3}{2}(1 + 0)}{(x + 1)^{\frac{5}{2}}})x + \frac{2}{(x + 1)^{\frac{3}{2}}}\\=&\frac{-9x^{2}}{4(x + 1)^{\frac{5}{2}}} + \frac{3x}{(x + 1)^{\frac{3}{2}}} - \frac{3x}{(x + 1)^{\frac{5}{2}}} + \frac{2}{(x + 1)^{\frac{3}{2}}}\\ \end{split}\end{equation} \]

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