There are 1 questions in this calculation: for each question, the 1 derivative of y is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{{e}^{y}(xsin(x) + ycos(x))}{({x}^{2} + {y}^{2})}\ with\ respect\ to\ y：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{x{e}^{y}sin(x)}{(x^{2} + y^{2})} + \frac{y{e}^{y}cos(x)}{(x^{2} + y^{2})}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{x{e}^{y}sin(x)}{(x^{2} + y^{2})} + \frac{y{e}^{y}cos(x)}{(x^{2} + y^{2})}\right)}{dy}\\=&(\frac{-(0 + 2y)}{(x^{2} + y^{2})^{2}})x{e}^{y}sin(x) + \frac{x({e}^{y}((1)ln(e) + \frac{(y)(0)}{(e)}))sin(x)}{(x^{2} + y^{2})} + \frac{x{e}^{y}cos(x)*0}{(x^{2} + y^{2})} + (\frac{-(0 + 2y)}{(x^{2} + y^{2})^{2}})y{e}^{y}cos(x) + \frac{{e}^{y}cos(x)}{(x^{2} + y^{2})} + \frac{y({e}^{y}((1)ln(e) + \frac{(y)(0)}{(e)}))cos(x)}{(x^{2} + y^{2})} + \frac{y{e}^{y}*-sin(x)*0}{(x^{2} + y^{2})}\\=&\frac{-2xy{e}^{y}sin(x)}{(x^{2} + y^{2})^{2}} + \frac{x{e}^{y}sin(x)}{(x^{2} + y^{2})} - \frac{2y^{2}{e}^{y}cos(x)}{(x^{2} + y^{2})^{2}} + \frac{{e}^{y}cos(x)}{(x^{2} + y^{2})} + \frac{y{e}^{y}cos(x)}{(x^{2} + y^{2})}\\ \end{split}\end{equation} \]

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