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

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