There are 1 questions in this calculation: for each question, the 2 derivative of t is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ cos(t)y(t) + sin(t)g(t)\ with\ respect\ to\ t：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = ytcos(t) + gtsin(t)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( ytcos(t) + gtsin(t)\right)}{dt}\\=&ycos(t) + yt*-sin(t) + gsin(t) + gtcos(t)\\=&ycos(t) - ytsin(t) + gsin(t) + gtcos(t)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( ycos(t) - ytsin(t) + gsin(t) + gtcos(t)\right)}{dt}\\=&y*-sin(t) - ysin(t) - ytcos(t) + gcos(t) + gcos(t) + gt*-sin(t)\\=&-2ysin(t) - ytcos(t) + 2gcos(t) - gtsin(t)\\ \end{split}\end{equation} \]

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