There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ {e}^{(\frac{ln(x + 1)}{x})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = {e}^{(\frac{ln(x + 1)}{x})}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( {e}^{(\frac{ln(x + 1)}{x})}\right)}{dx}\\=&({e}^{(\frac{ln(x + 1)}{x})}((\frac{-ln(x + 1)}{x^{2}} + \frac{(1 + 0)}{x(x + 1)})ln(e) + \frac{(\frac{ln(x + 1)}{x})(0)}{(e)}))\\=&\frac{-{e}^{(\frac{ln(x + 1)}{x})}ln(x + 1)}{x^{2}} + \frac{{e}^{(\frac{ln(x + 1)}{x})}}{(x + 1)x}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-{e}^{(\frac{ln(x + 1)}{x})}ln(x + 1)}{x^{2}} + \frac{{e}^{(\frac{ln(x + 1)}{x})}}{(x + 1)x}\right)}{dx}\\=&\frac{--2{e}^{(\frac{ln(x + 1)}{x})}ln(x + 1)}{x^{3}} - \frac{({e}^{(\frac{ln(x + 1)}{x})}((\frac{-ln(x + 1)}{x^{2}} + \frac{(1 + 0)}{x(x + 1)})ln(e) + \frac{(\frac{ln(x + 1)}{x})(0)}{(e)}))ln(x + 1)}{x^{2}} - \frac{{e}^{(\frac{ln(x + 1)}{x})}(1 + 0)}{x^{2}(x + 1)} + \frac{(\frac{-(1 + 0)}{(x + 1)^{2}}){e}^{(\frac{ln(x + 1)}{x})}}{x} + \frac{-{e}^{(\frac{ln(x + 1)}{x})}}{(x + 1)x^{2}} + \frac{({e}^{(\frac{ln(x + 1)}{x})}((\frac{-ln(x + 1)}{x^{2}} + \frac{(1 + 0)}{x(x + 1)})ln(e) + \frac{(\frac{ln(x + 1)}{x})(0)}{(e)}))}{(x + 1)x}\\=&\frac{2{e}^{(\frac{ln(x + 1)}{x})}ln(x + 1)}{x^{3}} + \frac{{e}^{(\frac{ln(x + 1)}{x})}ln^{2}(x + 1)}{x^{4}} - \frac{2{e}^{(\frac{ln(x + 1)}{x})}ln(x + 1)}{(x + 1)x^{3}} - \frac{2{e}^{(\frac{ln(x + 1)}{x})}}{(x + 1)x^{2}} - \frac{{e}^{(\frac{ln(x + 1)}{x})}}{(x + 1)^{2}x} + \frac{{e}^{(\frac{ln(x + 1)}{x})}}{(x + 1)^{2}x^{2}}\\ \end{split}\end{equation} \]

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