There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ (\frac{-1}{10})sin(5x) - (\frac{1}{2})xcos(5x) + cos(5x)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{-1}{10}sin(5x) - \frac{1}{2}xcos(5x) + cos(5x)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{-1}{10}sin(5x) - \frac{1}{2}xcos(5x) + cos(5x)\right)}{dx}\\=&\frac{-1}{10}cos(5x)*5 - \frac{1}{2}cos(5x) - \frac{1}{2}x*-sin(5x)*5 + -sin(5x)*5\\=&-cos(5x) + \frac{5xsin(5x)}{2} - 5sin(5x)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( -cos(5x) + \frac{5xsin(5x)}{2} - 5sin(5x)\right)}{dx}\\=&--sin(5x)*5 + \frac{5sin(5x)}{2} + \frac{5xcos(5x)*5}{2} - 5cos(5x)*5\\=&\frac{15sin(5x)}{2} + \frac{25xcos(5x)}{2} - 25cos(5x)\\ \end{split}\end{equation} \]

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