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

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