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

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