There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ sin(\frac{{x}^{x}}{({x}^{2}e^{x})})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = sin(\frac{{x}^{x}}{x^{2}e^{x}})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( sin(\frac{{x}^{x}}{x^{2}e^{x}})\right)}{dx}\\=&cos(\frac{{x}^{x}}{x^{2}e^{x}})(\frac{-2{x}^{x}}{x^{3}e^{x}} + \frac{({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{x^{2}e^{x}} + \frac{{x}^{x}*-e^{x}}{x^{2}e^{{x}*{2}}})\\=&\frac{-2{x}^{x}cos(\frac{{x}^{x}}{x^{2}e^{x}})}{x^{3}e^{x}} + \frac{{x}^{x}ln(x)cos(\frac{{x}^{x}}{x^{2}e^{x}})}{x^{2}e^{x}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-2{x}^{x}cos(\frac{{x}^{x}}{x^{2}e^{x}})}{x^{3}e^{x}} + \frac{{x}^{x}ln(x)cos(\frac{{x}^{x}}{x^{2}e^{x}})}{x^{2}e^{x}}\right)}{dx}\\=&\frac{-2*-3{x}^{x}cos(\frac{{x}^{x}}{x^{2}e^{x}})}{x^{4}e^{x}} - \frac{2({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))cos(\frac{{x}^{x}}{x^{2}e^{x}})}{x^{3}e^{x}} - \frac{2{x}^{x}*-e^{x}cos(\frac{{x}^{x}}{x^{2}e^{x}})}{x^{3}e^{{x}*{2}}} - \frac{2{x}^{x}*-sin(\frac{{x}^{x}}{x^{2}e^{x}})(\frac{-2{x}^{x}}{x^{3}e^{x}} + \frac{({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{x^{2}e^{x}} + \frac{{x}^{x}*-e^{x}}{x^{2}e^{{x}*{2}}})}{x^{3}e^{x}} + \frac{-2{x}^{x}ln(x)cos(\frac{{x}^{x}}{x^{2}e^{x}})}{x^{3}e^{x}} + \frac{({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))ln(x)cos(\frac{{x}^{x}}{x^{2}e^{x}})}{x^{2}e^{x}} + \frac{{x}^{x}*-e^{x}ln(x)cos(\frac{{x}^{x}}{x^{2}e^{x}})}{x^{2}e^{{x}*{2}}} + \frac{{x}^{x}cos(\frac{{x}^{x}}{x^{2}e^{x}})}{x^{2}e^{x}(x)} + \frac{{x}^{x}ln(x)*-sin(\frac{{x}^{x}}{x^{2}e^{x}})(\frac{-2{x}^{x}}{x^{3}e^{x}} + \frac{({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{x^{2}e^{x}} + \frac{{x}^{x}*-e^{x}}{x^{2}e^{{x}*{2}}})}{x^{2}e^{x}}\\=&\frac{6{x}^{x}cos(\frac{{x}^{x}}{x^{2}e^{x}})}{x^{4}e^{x}} - \frac{4{x}^{x}ln(x)cos(\frac{{x}^{x}}{x^{2}e^{x}})}{x^{3}e^{x}} + \frac{{x}^{x}cos(\frac{{x}^{x}}{x^{2}e^{x}})}{x^{3}e^{x}} - \frac{4{x}^{(2x)}sin(\frac{{x}^{x}}{x^{2}e^{x}})}{x^{6}e^{{x}*{2}}} + \frac{4{x}^{(2x)}ln(x)sin(\frac{{x}^{x}}{x^{2}e^{x}})}{x^{5}e^{{x}*{2}}} + \frac{{x}^{x}ln^{2}(x)cos(\frac{{x}^{x}}{x^{2}e^{x}})}{x^{2}e^{x}} - \frac{{x}^{(2x)}ln^{2}(x)sin(\frac{{x}^{x}}{x^{2}e^{x}})}{x^{4}e^{{x}*{2}}}\\ \end{split}\end{equation} \]

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