Partial Derivative – Calculating second order partial derivatives to a function inside a square root – Exercise 4320

z''_{xx} (x,y)=\frac{y^2}{{(x^2+y^2)}^{\frac{3}{2}}}

z''_{yy} (x,y)=\frac{x^2}{{(x^2+y^2)}^{\frac{3}{2}}}

z''_{xy} (x,y)=z''_{yx}(x,y)=\frac{-xy}{{(x^2+y^2)}^{\frac{3}{2}}}