# Partial Derivative – Calculating second order partial derivatives to a function inside a square root in a ln function – Exercise 4323

Exercise

Find  second order partial derivatives of the function

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

$$z''_{xx} (x,y)=\frac{y^2-x^2}{{(x^2+y^2)}^2}$$
$$z''_{yy} (x,y)=\frac{x^2-y^2}{{(x^2+y^2)}^2}$$
$$z''_{xy} (x,y)=z''_{yx}(x,y)=\frac{-2xy}{{(x^2+y^2)}^2}$$