There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
Note that variables are case sensitive.\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ 135e^{\frac{-109}{5}x}(cos(\frac{1601}{5}x) + \frac{1}{10}sin(\frac{1601}{5}x)) - 135cos(100πx - \frac{2}{5}π)\ with\ respect\ to\ x:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 135e^{\frac{-109}{5}x}cos(\frac{1601}{5}x) + \frac{27}{2}e^{\frac{-109}{5}x}sin(\frac{1601}{5}x) - 135cos(100πx - \frac{2}{5}π)\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( 135e^{\frac{-109}{5}x}cos(\frac{1601}{5}x) + \frac{27}{2}e^{\frac{-109}{5}x}sin(\frac{1601}{5}x) - 135cos(100πx - \frac{2}{5}π)\right)}{dx}\\=&135e^{\frac{-109}{5}x}*\frac{-109}{5}cos(\frac{1601}{5}x) + 135e^{\frac{-109}{5}x}*-sin(\frac{1601}{5}x)*\frac{1601}{5} + \frac{27}{2}e^{\frac{-109}{5}x}*\frac{-109}{5}sin(\frac{1601}{5}x) + \frac{27}{2}e^{\frac{-109}{5}x}cos(\frac{1601}{5}x)*\frac{1601}{5} - 135*-sin(100πx - \frac{2}{5}π)(100π + 0)\\=&\frac{13797e^{\frac{-109}{5}x}cos(\frac{1601}{5}x)}{10} - \frac{435213e^{\frac{-109}{5}x}sin(\frac{1601}{5}x)}{10} + 13500πsin(100πx - \frac{2}{5}π)\\ \end{split}\end{equation} \]Your problem has not been solved here? Please go to the Hot Problems section!