Chapter 14: Partial Derivatives - Practice Exercises - Page 864: 27

$f_{xx}=-30x+\frac{2-2x^{2}}{(x^{2}+1)^{2}}$ $f_{yy}=0$ $f_{xy}=f_{yx}=1$

$f(x,y)=x+xy-5x^{3}+\ln(x^{2}+1)$ $f_{x}=1+y-15x^{2}+\frac{2x}{x^{2}+1}$ $f_{xx}=-30x+\frac{2-2x^{2}}{(x^{2}+1)^{2}}$ $f_{yx}=1$ $f_{y}=x$ $f_{yy}=0$ $f_{xy}=f_{yx}$