There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ 12{(\frac{2}{5}{x}^{(\frac{-1}{2})} + \frac{3}{5}{z}^{(\frac{-1}{2})})}^{-2}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{12}{(\frac{\frac{2}{5}}{x^{\frac{1}{2}}} + \frac{\frac{3}{5}}{z^{\frac{1}{2}}})^{2}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{12}{(\frac{\frac{2}{5}}{x^{\frac{1}{2}}} + \frac{\frac{3}{5}}{z^{\frac{1}{2}}})^{2}}\right)}{dx}\\=&12(\frac{-2(\frac{\frac{2}{5}*\frac{-1}{2}}{x^{\frac{3}{2}}} + 0)}{(\frac{\frac{2}{5}}{x^{\frac{1}{2}}} + \frac{\frac{3}{5}}{z^{\frac{1}{2}}})^{3}})\\=&\frac{24}{5(\frac{\frac{2}{5}}{x^{\frac{1}{2}}} + \frac{\frac{3}{5}}{z^{\frac{1}{2}}})^{3}x^{\frac{3}{2}}}\\ \end{split}\end{equation} \]

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