There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ sin(sin(sin(sqrt(\frac{1}{({x}^{2} + 1)}))))\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = sin(sin(sin(sqrt(\frac{1}{(x^{2} + 1)}))))\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( sin(sin(sin(sqrt(\frac{1}{(x^{2} + 1)}))))\right)}{dx}\\=&\frac{cos(sin(sin(sqrt(\frac{1}{(x^{2} + 1)}))))cos(sin(sqrt(\frac{1}{(x^{2} + 1)})))cos(sqrt(\frac{1}{(x^{2} + 1)}))(\frac{-(2x + 0)}{(x^{2} + 1)^{2}})*\frac{1}{2}}{(\frac{1}{(x^{2} + 1)})^{\frac{1}{2}}}\\=&\frac{-xcos(sin(sin(sqrt(\frac{1}{(x^{2} + 1)}))))cos(sqrt(\frac{1}{(x^{2} + 1)}))cos(sin(sqrt(\frac{1}{(x^{2} + 1)})))}{(x^{2} + 1)^{\frac{3}{2}}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-xcos(sin(sin(sqrt(\frac{1}{(x^{2} + 1)}))))cos(sqrt(\frac{1}{(x^{2} + 1)}))cos(sin(sqrt(\frac{1}{(x^{2} + 1)})))}{(x^{2} + 1)^{\frac{3}{2}}}\right)}{dx}\\=&-(\frac{\frac{-3}{2}(2x + 0)}{(x^{2} + 1)^{\frac{5}{2}}})xcos(sin(sin(sqrt(\frac{1}{(x^{2} + 1)}))))cos(sqrt(\frac{1}{(x^{2} + 1)}))cos(sin(sqrt(\frac{1}{(x^{2} + 1)}))) - \frac{cos(sin(sin(sqrt(\frac{1}{(x^{2} + 1)}))))cos(sqrt(\frac{1}{(x^{2} + 1)}))cos(sin(sqrt(\frac{1}{(x^{2} + 1)})))}{(x^{2} + 1)^{\frac{3}{2}}} - \frac{x*-sin(sin(sin(sqrt(\frac{1}{(x^{2} + 1)}))))cos(sin(sqrt(\frac{1}{(x^{2} + 1)})))cos(sqrt(\frac{1}{(x^{2} + 1)}))(\frac{-(2x + 0)}{(x^{2} + 1)^{2}})*\frac{1}{2}cos(sqrt(\frac{1}{(x^{2} + 1)}))cos(sin(sqrt(\frac{1}{(x^{2} + 1)})))}{(x^{2} + 1)^{\frac{3}{2}}(\frac{1}{(x^{2} + 1)})^{\frac{1}{2}}} - \frac{xcos(sin(sin(sqrt(\frac{1}{(x^{2} + 1)}))))*-sin(sqrt(\frac{1}{(x^{2} + 1)}))(\frac{-(2x + 0)}{(x^{2} + 1)^{2}})*\frac{1}{2}cos(sin(sqrt(\frac{1}{(x^{2} + 1)})))}{(x^{2} + 1)^{\frac{3}{2}}(\frac{1}{(x^{2} + 1)})^{\frac{1}{2}}} - \frac{xcos(sin(sin(sqrt(\frac{1}{(x^{2} + 1)}))))cos(sqrt(\frac{1}{(x^{2} + 1)}))*-sin(sin(sqrt(\frac{1}{(x^{2} + 1)})))cos(sqrt(\frac{1}{(x^{2} + 1)}))(\frac{-(2x + 0)}{(x^{2} + 1)^{2}})*\frac{1}{2}}{(x^{2} + 1)^{\frac{3}{2}}(\frac{1}{(x^{2} + 1)})^{\frac{1}{2}}}\\=&\frac{3x^{2}cos(sin(sin(sqrt(\frac{1}{(x^{2} + 1)}))))cos(sqrt(\frac{1}{(x^{2} + 1)}))cos(sin(sqrt(\frac{1}{(x^{2} + 1)})))}{(x^{2} + 1)^{\frac{5}{2}}} - \frac{cos(sin(sin(sqrt(\frac{1}{(x^{2} + 1)}))))cos(sqrt(\frac{1}{(x^{2} + 1)}))cos(sin(sqrt(\frac{1}{(x^{2} + 1)})))}{(x^{2} + 1)^{\frac{3}{2}}} - \frac{x^{2}sin(sin(sin(sqrt(\frac{1}{(x^{2} + 1)}))))cos^{2}(sin(sqrt(\frac{1}{(x^{2} + 1)})))cos^{2}(sqrt(\frac{1}{(x^{2} + 1)}))}{(x^{2} + 1)^{3}} - \frac{x^{2}sin(sqrt(\frac{1}{(x^{2} + 1)}))cos(sin(sin(sqrt(\frac{1}{(x^{2} + 1)}))))cos(sin(sqrt(\frac{1}{(x^{2} + 1)})))}{(x^{2} + 1)^{3}} - \frac{x^{2}sin(sin(sqrt(\frac{1}{(x^{2} + 1)})))cos(sin(sin(sqrt(\frac{1}{(x^{2} + 1)}))))cos^{2}(sqrt(\frac{1}{(x^{2} + 1)}))}{(x^{2} + 1)^{3}}\\ \end{split}\end{equation} \]

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