## Calculus 8th Edition

Given: $f_{x}=x+y^{2}$ and $f_{y}=x-y^{2}$ Take second derivative of the function with respect to $y$ keeping $x$ constant. $f_{xy}=1$ $f_{y}=x-y^{2}$ Take second derivative of the function with respect to $x$ keeping $y$ constant. $f_{yx}=2y$ Thus, $f_{xy} \ne f_{yx}$ Thus , the second derivative of the function f does not verified the Clairaut's Theorem, that is, $f_{xy} = f_{yx}$ Hence, the statement is false.