There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ ({x}^{2} + 2{y}^{2} + 3{z}^{2}){e}^{(-({x}^{2} + {y}^{2} + {z}^{2}))}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = x^{2}{e}^{(-x^{2} - y^{2} - z^{2})} + 2y^{2}{e}^{(-x^{2} - y^{2} - z^{2})} + 3z^{2}{e}^{(-x^{2} - y^{2} - z^{2})}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( x^{2}{e}^{(-x^{2} - y^{2} - z^{2})} + 2y^{2}{e}^{(-x^{2} - y^{2} - z^{2})} + 3z^{2}{e}^{(-x^{2} - y^{2} - z^{2})}\right)}{dx}\\=&2x{e}^{(-x^{2} - y^{2} - z^{2})} + x^{2}({e}^{(-x^{2} - y^{2} - z^{2})}((-2x + 0 + 0)ln(e) + \frac{(-x^{2} - y^{2} - z^{2})(0)}{(e)})) + 2y^{2}({e}^{(-x^{2} - y^{2} - z^{2})}((-2x + 0 + 0)ln(e) + \frac{(-x^{2} - y^{2} - z^{2})(0)}{(e)})) + 3z^{2}({e}^{(-x^{2} - y^{2} - z^{2})}((-2x + 0 + 0)ln(e) + \frac{(-x^{2} - y^{2} - z^{2})(0)}{(e)}))\\=&2x{e}^{(-x^{2} - y^{2} - z^{2})} - 2x^{3}{e}^{(-x^{2} - y^{2} - z^{2})} - 4y^{2}x{e}^{(-x^{2} - y^{2} - z^{2})} - 6z^{2}x{e}^{(-x^{2} - y^{2} - z^{2})}\\ \end{split}\end{equation} \]

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