There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ 6ln({e}^{(\frac{-1000}{x})} - {e}^{(\frac{-2000}{x})})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 6ln({e}^{(\frac{-1000}{x})} - {e}^{(\frac{-2000}{x})})\right)}{dx}\\=&\frac{6(({e}^{(\frac{-1000}{x})}((\frac{-1000*-1}{x^{2}})ln(e) + \frac{(\frac{-1000}{x})(0)}{(e)})) - ({e}^{(\frac{-2000}{x})}((\frac{-2000*-1}{x^{2}})ln(e) + \frac{(\frac{-2000}{x})(0)}{(e)})))}{({e}^{(\frac{-1000}{x})} - {e}^{(\frac{-2000}{x})})}\\=&\frac{6000{e}^{(\frac{-1000}{x})}}{({e}^{(\frac{-1000}{x})} - {e}^{(\frac{-2000}{x})})x^{2}} - \frac{12000{e}^{(\frac{-2000}{x})}}{({e}^{(\frac{-1000}{x})} - {e}^{(\frac{-2000}{x})})x^{2}}\\ \end{split}\end{equation} \]

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