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

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