There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ sin({x}^{2} + {y}^{2}){e}^{(\frac{-1}{10}({x}^{2} + {y}^{2} + xy + 2x))}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = {e}^{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)}sin(x^{2} + y^{2})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( {e}^{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)}sin(x^{2} + y^{2})\right)}{dx}\\=&({e}^{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)}((\frac{-1}{10}*2x - \frac{1}{10}y + 0 - \frac{1}{5})ln(e) + \frac{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)(0)}{(e)}))sin(x^{2} + y^{2}) + {e}^{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)}cos(x^{2} + y^{2})(2x + 0)\\=&\frac{-x{e}^{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)}sin(x^{2} + y^{2})}{5} - \frac{y{e}^{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)}sin(x^{2} + y^{2})}{10} - \frac{{e}^{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)}sin(x^{2} + y^{2})}{5} + 2x{e}^{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)}cos(x^{2} + y^{2})\\ \end{split}\end{equation} \]

Your problem has not been solved here? Please take a look at the  hot problems ！