There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ e^{x}cos(\frac{x}{1000}) - \frac{e^{x}sin(\frac{x}{1000})}{1000}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = e^{x}cos(\frac{1}{1000}x) - \frac{1}{1000}e^{x}sin(\frac{1}{1000}x)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( e^{x}cos(\frac{1}{1000}x) - \frac{1}{1000}e^{x}sin(\frac{1}{1000}x)\right)}{dx}\\=&e^{x}cos(\frac{1}{1000}x) + e^{x}*-sin(\frac{1}{1000}x)*\frac{1}{1000} - \frac{1}{1000}e^{x}sin(\frac{1}{1000}x) - \frac{1}{1000}e^{x}cos(\frac{1}{1000}x)*\frac{1}{1000}\\=&\frac{999999e^{x}cos(\frac{1}{1000}x)}{1000000} - \frac{e^{x}sin(\frac{1}{1000}x)}{500}\\ \end{split}\end{equation} \]

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