There are 1 questions in this calculation: for each question, the 1 derivative of t is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ 3cos(4t) + 2sin(4t) + 5tsin(4t)\ with\ respect\ to\ t：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 3cos(4t) + 2sin(4t) + 5tsin(4t)\right)}{dt}\\=&3*-sin(4t)*4 + 2cos(4t)*4 + 5sin(4t) + 5tcos(4t)*4\\=&-7sin(4t) + 8cos(4t) + 20tcos(4t)\\ \end{split}\end{equation} \]

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