There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ (\frac{1}{(ab)}){e}^{(\frac{-({(x - c)}^{2})}{(2({a}^{2}))})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{{e}^{(\frac{\frac{-1}{2}x^{2}}{a^{2}} + \frac{cx}{a^{2}} - \frac{\frac{1}{2}c^{2}}{a^{2}})}}{ab}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{{e}^{(\frac{\frac{-1}{2}x^{2}}{a^{2}} + \frac{cx}{a^{2}} - \frac{\frac{1}{2}c^{2}}{a^{2}})}}{ab}\right)}{dx}\\=&\frac{({e}^{(\frac{\frac{-1}{2}x^{2}}{a^{2}} + \frac{cx}{a^{2}} - \frac{\frac{1}{2}c^{2}}{a^{2}})}((\frac{\frac{-1}{2}*2x}{a^{2}} + \frac{c}{a^{2}} + 0)ln(e) + \frac{(\frac{\frac{-1}{2}x^{2}}{a^{2}} + \frac{cx}{a^{2}} - \frac{\frac{1}{2}c^{2}}{a^{2}})(0)}{(e)}))}{ab}\\=&\frac{-x{e}^{(\frac{\frac{-1}{2}x^{2}}{a^{2}} + \frac{cx}{a^{2}} - \frac{\frac{1}{2}c^{2}}{a^{2}})}}{a^{3}b} + \frac{c{e}^{(\frac{\frac{-1}{2}x^{2}}{a^{2}} + \frac{cx}{a^{2}} - \frac{\frac{1}{2}c^{2}}{a^{2}})}}{a^{3}b}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-x{e}^{(\frac{\frac{-1}{2}x^{2}}{a^{2}} + \frac{cx}{a^{2}} - \frac{\frac{1}{2}c^{2}}{a^{2}})}}{a^{3}b} + \frac{c{e}^{(\frac{\frac{-1}{2}x^{2}}{a^{2}} + \frac{cx}{a^{2}} - \frac{\frac{1}{2}c^{2}}{a^{2}})}}{a^{3}b}\right)}{dx}\\=&\frac{-{e}^{(\frac{\frac{-1}{2}x^{2}}{a^{2}} + \frac{cx}{a^{2}} - \frac{\frac{1}{2}c^{2}}{a^{2}})}}{a^{3}b} - \frac{x({e}^{(\frac{\frac{-1}{2}x^{2}}{a^{2}} + \frac{cx}{a^{2}} - \frac{\frac{1}{2}c^{2}}{a^{2}})}((\frac{\frac{-1}{2}*2x}{a^{2}} + \frac{c}{a^{2}} + 0)ln(e) + \frac{(\frac{\frac{-1}{2}x^{2}}{a^{2}} + \frac{cx}{a^{2}} - \frac{\frac{1}{2}c^{2}}{a^{2}})(0)}{(e)}))}{a^{3}b} + \frac{c({e}^{(\frac{\frac{-1}{2}x^{2}}{a^{2}} + \frac{cx}{a^{2}} - \frac{\frac{1}{2}c^{2}}{a^{2}})}((\frac{\frac{-1}{2}*2x}{a^{2}} + \frac{c}{a^{2}} + 0)ln(e) + \frac{(\frac{\frac{-1}{2}x^{2}}{a^{2}} + \frac{cx}{a^{2}} - \frac{\frac{1}{2}c^{2}}{a^{2}})(0)}{(e)}))}{a^{3}b}\\=&\frac{-{e}^{(\frac{\frac{-1}{2}x^{2}}{a^{2}} + \frac{cx}{a^{2}} - \frac{\frac{1}{2}c^{2}}{a^{2}})}}{a^{3}b} + \frac{x^{2}{e}^{(\frac{\frac{-1}{2}x^{2}}{a^{2}} + \frac{cx}{a^{2}} - \frac{\frac{1}{2}c^{2}}{a^{2}})}}{a^{5}b} - \frac{2cx{e}^{(\frac{\frac{-1}{2}x^{2}}{a^{2}} + \frac{cx}{a^{2}} - \frac{\frac{1}{2}c^{2}}{a^{2}})}}{a^{5}b} + \frac{c^{2}{e}^{(\frac{\frac{-1}{2}x^{2}}{a^{2}} + \frac{cx}{a^{2}} - \frac{\frac{1}{2}c^{2}}{a^{2}})}}{a^{5}b}\\ \end{split}\end{equation} \]

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