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

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