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

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