Найти полный дифференциал функции

[latex]z=ln(x+\sqrt{x^2+y^2})\\\\z'_{x}= \frac{1+\frac{2x}{2\sqrt{x^2+y^2}}}{x+\sqrt{x^2+y^2}} = \frac{x+\sqrt{x^2+y^2}}{\sqrt{x^2+y^2}\cdot (x+\sqrt{x^2+y^2}))} =\frac{1}{\sqrt{x^2+y^2}}\\\\z'_{y}= \frac{\frac{2y}{2\sqrt{x^2+y^2}}}{x+\sqrt{x^2+y^2}} = \frac{y}{\sqrt{x^2+y^2}(x+\sqrt{x^2+y^2})} }\\\\dz=z'_{x}dx+z'_{y}dy=\frac{dx}{\sqrt{x^2+y^2}}+\frac{y\, dy}{\sqrt{x^2+y^2}(x+\sqrt{x^2+y^2})}\\[/latex]