There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
Note that variables are case sensitive.\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ sin(x) + \frac{sin(2x)}{2} + \frac{sin(3x)}{3} + \frac{sin(4x)}{4} + \frac{sin(5x)}{5} + \frac{sin(6x)}{6}\ with\ respect\ to\ x:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = sin(x) + \frac{1}{2}sin(2x) + \frac{1}{3}sin(3x) + \frac{1}{4}sin(4x) + \frac{1}{5}sin(5x) + \frac{1}{6}sin(6x)\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( sin(x) + \frac{1}{2}sin(2x) + \frac{1}{3}sin(3x) + \frac{1}{4}sin(4x) + \frac{1}{5}sin(5x) + \frac{1}{6}sin(6x)\right)}{dx}\\=&cos(x) + \frac{1}{2}cos(2x)*2 + \frac{1}{3}cos(3x)*3 + \frac{1}{4}cos(4x)*4 + \frac{1}{5}cos(5x)*5 + \frac{1}{6}cos(6x)*6\\=&cos(x) + cos(2x) + cos(3x) + cos(4x) + cos(5x) + cos(6x)\\ \end{split}\end{equation} \]Your problem has not been solved here? Please go to the Hot Problems section!