There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ \frac{-1}{sqrt(u{(cos(x))}^{2} + {(sin(x))}^{2})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{-1}{sqrt(ucos^{2}(x) + sin^{2}(x))}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{-1}{sqrt(ucos^{2}(x) + sin^{2}(x))}\right)}{dx}\\=&\frac{--(u*-2cos(x)sin(x) + 2sin(x)cos(x))*\frac{1}{2}}{(ucos^{2}(x) + sin^{2}(x))(ucos^{2}(x) + sin^{2}(x))^{\frac{1}{2}}}\\=&\frac{-usin(x)cos(x)}{(ucos^{2}(x) + sin^{2}(x))^{\frac{3}{2}}} + \frac{sin(x)cos(x)}{(ucos^{2}(x) + sin^{2}(x))^{\frac{3}{2}}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-usin(x)cos(x)}{(ucos^{2}(x) + sin^{2}(x))^{\frac{3}{2}}} + \frac{sin(x)cos(x)}{(ucos^{2}(x) + sin^{2}(x))^{\frac{3}{2}}}\right)}{dx}\\=&-(\frac{\frac{-3}{2}(u*-2cos(x)sin(x) + 2sin(x)cos(x))}{(ucos^{2}(x) + sin^{2}(x))^{\frac{5}{2}}})usin(x)cos(x) - \frac{ucos(x)cos(x)}{(ucos^{2}(x) + sin^{2}(x))^{\frac{3}{2}}} - \frac{usin(x)*-sin(x)}{(ucos^{2}(x) + sin^{2}(x))^{\frac{3}{2}}} + (\frac{\frac{-3}{2}(u*-2cos(x)sin(x) + 2sin(x)cos(x))}{(ucos^{2}(x) + sin^{2}(x))^{\frac{5}{2}}})sin(x)cos(x) + \frac{cos(x)cos(x)}{(ucos^{2}(x) + sin^{2}(x))^{\frac{3}{2}}} + \frac{sin(x)*-sin(x)}{(ucos^{2}(x) + sin^{2}(x))^{\frac{3}{2}}}\\=&\frac{-3u^{2}sin^{2}(x)cos^{2}(x)}{(ucos^{2}(x) + sin^{2}(x))^{\frac{5}{2}}} + \frac{6usin^{2}(x)cos^{2}(x)}{(ucos^{2}(x) + sin^{2}(x))^{\frac{5}{2}}} - \frac{ucos^{2}(x)}{(ucos^{2}(x) + sin^{2}(x))^{\frac{3}{2}}} + \frac{usin^{2}(x)}{(ucos^{2}(x) + sin^{2}(x))^{\frac{3}{2}}} - \frac{3sin^{2}(x)cos^{2}(x)}{(ucos^{2}(x) + sin^{2}(x))^{\frac{5}{2}}} + \frac{cos^{2}(x)}{(ucos^{2}(x) + sin^{2}(x))^{\frac{3}{2}}} - \frac{sin^{2}(x)}{(ucos^{2}(x) + sin^{2}(x))^{\frac{3}{2}}}\\ \end{split}\end{equation} \]

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