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





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