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

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