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

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