There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ e^{(-1){\frac{1}{(\frac{x}{1000})}}^{(\frac{x}{1000})}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = e^{-(\frac{1000}{x})^{(\frac{1}{1000}x)}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( e^{-(\frac{1000}{x})^{(\frac{1}{1000}x)}}\right)}{dx}\\=&e^{-(\frac{1000}{x})^{(\frac{1}{1000}x)}}*-((\frac{1000}{x})^{(\frac{1}{1000}x)}((\frac{1}{1000})ln(\frac{1000}{x}) + \frac{(\frac{1}{1000}x)(\frac{1000*-1}{x^{2}})}{(\frac{1000}{x})}))\\=&\frac{-(\frac{1000}{x})^{(\frac{1}{1000}x)}e^{-(\frac{1000}{x})^{(\frac{1}{1000}x)}}ln(\frac{1000}{x})}{1000} + \frac{(\frac{1000}{x})^{(\frac{1}{1000}x)}e^{-(\frac{1000}{x})^{(\frac{1}{1000}x)}}}{1000}\\ \end{split}\end{equation} \]

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