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

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