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

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