f(x,y)= arctan(y/x)

Im familiar with "outer" and "inner" derivates and usually know how to work them. I also know that the derivative of arctan = 1/(1+x^2)

so i get

f'x= 1/(1+x^2) * (y/x) * ??

What is the x-derivative of y/x ?

I also cannot seem to find the partial derivates to:

f(x,y)= (x+y)/(x-y)

Help would be highly appreciated...