# Partial Derivative – A quotient of functions inside arcsin function – Exercise 3294

Exercise

Find partial derivatives of the function

$$z(x,y)=\arcsin\frac{x}{\sqrt{x^2+y^2}}$$

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