Chain rule and cylindrical coordinates

[cycling4life]

I'm trying to understand this one derivation but this one part keeps messing me up;

theta = tan^-1 (y/x)
r^2 = x^2 + y^2

d theta/ d x = y/ (x^2 + y^2) how did they get this line?

 

[Char. Limit]

You just need to differentiate arctan(y/x) wrt x. Assume y is a constant for the purposes of this integration, of course.