There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ \frac{(xy + {e}^{(xy)})}{(sec(x)sec(x))}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{yx}{sec^{2}(x)} + \frac{{e}^{(yx)}}{sec^{2}(x)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{yx}{sec^{2}(x)} + \frac{{e}^{(yx)}}{sec^{2}(x)}\right)}{dx}\\=&\frac{y}{sec^{2}(x)} + \frac{yx*-2tan(x)}{sec^{2}(x)} + \frac{({e}^{(yx)}((y)ln(e) + \frac{(yx)(0)}{(e)}))}{sec^{2}(x)} + \frac{{e}^{(yx)}*-2tan(x)}{sec^{2}(x)}\\=&\frac{y}{sec^{2}(x)} - \frac{2yxtan(x)}{sec^{2}(x)} + \frac{y{e}^{(yx)}}{sec^{2}(x)} - \frac{2{e}^{(yx)}tan(x)}{sec^{2}(x)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{y}{sec^{2}(x)} - \frac{2yxtan(x)}{sec^{2}(x)} + \frac{y{e}^{(yx)}}{sec^{2}(x)} - \frac{2{e}^{(yx)}tan(x)}{sec^{2}(x)}\right)}{dx}\\=&\frac{y*-2tan(x)}{sec^{2}(x)} - \frac{2ytan(x)}{sec^{2}(x)} - \frac{2yxsec^{2}(x)(1)}{sec^{2}(x)} - \frac{2yxtan(x)*-2tan(x)}{sec^{2}(x)} + \frac{y({e}^{(yx)}((y)ln(e) + \frac{(yx)(0)}{(e)}))}{sec^{2}(x)} + \frac{y{e}^{(yx)}*-2tan(x)}{sec^{2}(x)} - \frac{2({e}^{(yx)}((y)ln(e) + \frac{(yx)(0)}{(e)}))tan(x)}{sec^{2}(x)} - \frac{2{e}^{(yx)}sec^{2}(x)(1)}{sec^{2}(x)} - \frac{2{e}^{(yx)}tan(x)*-2tan(x)}{sec^{2}(x)}\\=&\frac{-4ytan(x)}{sec^{2}(x)} + \frac{4yxtan^{2}(x)}{sec^{2}(x)} - 2yx + \frac{y^{2}{e}^{(yx)}}{sec^{2}(x)} - \frac{4y{e}^{(yx)}tan(x)}{sec^{2}(x)} + \frac{4{e}^{(yx)}tan^{2}(x)}{sec^{2}(x)} - 2{e}^{(yx)}\\ \end{split}\end{equation} \]

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