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

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