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

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