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

Your problem has not been solved here? Please take a look at the  hot problems ！