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

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