There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ 20{\frac{1}{x}}^{\frac{5}{2}} - 15{\frac{1}{x}}^{5} + \frac{3{\frac{1}{x}}^{1}}{3}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{20}{x^{\frac{5}{2}}} - \frac{15}{x^{5}} + \frac{1}{x}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{20}{x^{\frac{5}{2}}} - \frac{15}{x^{5}} + \frac{1}{x}\right)}{dx}\\=&\frac{20*\frac{-5}{2}}{x^{\frac{7}{2}}} - \frac{15*-5}{x^{6}} + \frac{-1}{x^{2}}\\=&\frac{-50}{x^{\frac{7}{2}}} + \frac{75}{x^{6}} - \frac{1}{x^{2}}\\ \end{split}\end{equation} \]

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