There are 1 questions in this calculation: for each question, the 2 derivative of t is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ 2cos(5t) - 2sin(5t) + 5tsin(5t)\ with\ respect\ to\ t：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 2cos(5t) - 2sin(5t) + 5tsin(5t)\right)}{dt}\\=&2*-sin(5t)*5 - 2cos(5t)*5 + 5sin(5t) + 5tcos(5t)*5\\=&-5sin(5t) - 10cos(5t) + 25tcos(5t)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( -5sin(5t) - 10cos(5t) + 25tcos(5t)\right)}{dt}\\=&-5cos(5t)*5 - 10*-sin(5t)*5 + 25cos(5t) + 25t*-sin(5t)*5\\=&50sin(5t) - 125tsin(5t)\\ \end{split}\end{equation} \]

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