There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ {ln(x)}^{2} + xcos(4x)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = ln^{2}(x) + xcos(4x)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( ln^{2}(x) + xcos(4x)\right)}{dx}\\=&\frac{2ln(x)}{(x)} + cos(4x) + x*-sin(4x)*4\\=&\frac{2ln(x)}{x} + cos(4x) - 4xsin(4x)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{2ln(x)}{x} + cos(4x) - 4xsin(4x)\right)}{dx}\\=&\frac{2*-ln(x)}{x^{2}} + \frac{2}{x(x)} + -sin(4x)*4 - 4sin(4x) - 4xcos(4x)*4\\=&\frac{-2ln(x)}{x^{2}} - 16xcos(4x) - 8sin(4x) + \frac{2}{x^{2}}\\ \end{split}\end{equation} \]

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