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

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