There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{((x - 2){\frac{1}{x}}^{\frac{5}{2}})}{({\frac{1}{(x + 1)}}^{\frac{3}{2}})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{(x + 1)^{\frac{3}{2}}}{x^{\frac{3}{2}}} - \frac{2(x + 1)^{\frac{3}{2}}}{x^{\frac{5}{2}}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{(x + 1)^{\frac{3}{2}}}{x^{\frac{3}{2}}} - \frac{2(x + 1)^{\frac{3}{2}}}{x^{\frac{5}{2}}}\right)}{dx}\\=&\frac{(\frac{3}{2}(x + 1)^{\frac{1}{2}}(1 + 0))}{x^{\frac{3}{2}}} + \frac{(x + 1)^{\frac{3}{2}}*\frac{-3}{2}}{x^{\frac{5}{2}}} - \frac{2(\frac{3}{2}(x + 1)^{\frac{1}{2}}(1 + 0))}{x^{\frac{5}{2}}} - \frac{2(x + 1)^{\frac{3}{2}}*\frac{-5}{2}}{x^{\frac{7}{2}}}\\=&\frac{3(x + 1)^{\frac{1}{2}}}{2x^{\frac{3}{2}}} - \frac{3(x + 1)^{\frac{3}{2}}}{2x^{\frac{5}{2}}} - \frac{3(x + 1)^{\frac{1}{2}}}{x^{\frac{5}{2}}} + \frac{5(x + 1)^{\frac{3}{2}}}{x^{\frac{7}{2}}}\\ \end{split}\end{equation} \]

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