Answer
$$f_{xx}=-30x+\frac{2-2x^{2}}{(x^{2}+1)^{2}}; \\f_{yy}=0 ; \\f_{xy}=f_{yx}=1$$
Work Step by Step
$$f_{x}=1+y-15x^{2}+\dfrac{2x}{x^{2}+1}; \\f_{xx}=-30x+\dfrac{2-2x^{2}}{(x^{2}+1)^{2}}; \\f_{yx}=1; \\f_{y}=x \\f_{yy}=0 \\f_{xy}=f_{yx}$$
The second partial derivatives are as follows:
$$f_{xx}=-30x+\frac{2-2x^{2}}{(x^{2}+1)^{2}}; \\f_{yy}=0 ; \\f_{xy}=f_{yx}=1$$
