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

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