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

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