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

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