There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{({x}^{2} + {y}^{2})sin(1){\frac{1}{({x}^{2} + {y}^{2})}}^{1}}{2}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{\frac{1}{2}x^{2}sin(1)}{(x^{2} + y^{2})} + \frac{\frac{1}{2}y^{2}sin(1)}{(x^{2} + y^{2})}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{\frac{1}{2}x^{2}sin(1)}{(x^{2} + y^{2})} + \frac{\frac{1}{2}y^{2}sin(1)}{(x^{2} + y^{2})}\right)}{dx}\\=&\frac{1}{2}(\frac{-(2x + 0)}{(x^{2} + y^{2})^{2}})x^{2}sin(1) + \frac{\frac{1}{2}*2xsin(1)}{(x^{2} + y^{2})} + \frac{\frac{1}{2}x^{2}cos(1)*0}{(x^{2} + y^{2})} + \frac{1}{2}(\frac{-(2x + 0)}{(x^{2} + y^{2})^{2}})y^{2}sin(1) + \frac{\frac{1}{2}y^{2}cos(1)*0}{(x^{2} + y^{2})}\\=&\frac{-x^{3}sin(1)}{(x^{2} + y^{2})^{2}} + \frac{xsin(1)}{(x^{2} + y^{2})} - \frac{y^{2}xsin(1)}{(x^{2} + y^{2})^{2}}\\ \end{split}\end{equation} \]

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