Partial Derivative – y divided by x inside arctan function – Exercise 3284

Exercise

Find the partial derivatives of the function

$$z(x,y)=\arctan\frac{y}{x}$$

$$z'_x (x,y)=\frac{-y}{x^2+y^2}$$
$$z'_y (x,y)=\frac{x}{x^2+y^2}$$